python: hmm/hmm.py annotate

annotate hmm/hmm.py @ 69:157f012ffab7 default tip

from local

author	Henry S Thompson <ht@inf.ed.ac.uk>
date	Fri, 17 Jan 2025 15:45:26 +0000
parents	26d9c0308fcf
children

rev	line source
3 26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1 # Natural Language Toolkit: Hidden Markov Model
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	2 #
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	3 # Copyright (C) 2001-2015 NLTK Project
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	4 # Author: Trevor Cohn <tacohn@csse.unimelb.edu.au>
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	5 # Philip Blunsom <pcbl@csse.unimelb.edu.au>
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	6 # Tiago Tresoldi <tiago@tresoldi.pro.br> (fixes)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	7 # Steven Bird <stevenbird1@gmail.com> (fixes)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	8 # Joseph Frazee <jfrazee@mail.utexas.edu> (fixes)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	9 # Steven Xu <xxu@student.unimelb.edu.au> (fixes)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	10 # URL: <http://nltk.org/>
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	11 # For license information, see LICENSE.TXT
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	12
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	13 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	14 Hidden Markov Models (HMMs) largely used to assign the correct label sequence
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	15 to sequential data or assess the probability of a given label and data
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	16 sequence. These models are finite state machines characterised by a number of
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	17 states, transitions between these states, and output symbols emitted while in
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	18 each state. The HMM is an extension to the Markov chain, where each state
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	19 corresponds deterministically to a given event. In the HMM the observation is
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	20 a probabilistic function of the state. HMMs share the Markov chain's
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	21 assumption, being that the probability of transition from one state to another
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	22 only depends on the current state - i.e. the series of states that led to the
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	23 current state are not used. They are also time invariant.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	24
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	25 The HMM is a directed graph, with probability weighted edges (representing the
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	26 probability of a transition between the source and sink states) where each
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	27 vertex emits an output symbol when entered. The symbol (or observation) is
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	28 non-deterministically generated. For this reason, knowing that a sequence of
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	29 output observations was generated by a given HMM does not mean that the
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	30 corresponding sequence of states (and what the current state is) is known.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	31 This is the 'hidden' in the hidden markov model.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	32
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	33 Formally, a HMM can be characterised by:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	34
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	35 - the output observation alphabet. This is the set of symbols which may be
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	36 observed as output of the system.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	37 - the set of states.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	38 - the transition probabilities a_{ij} = P(s_t = j \| s_{t-1} = i). These
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	39 represent the probability of transition to each state from a given state.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	40 - the output probability matrix b_i(k) = P(X_t = o_k \| s_t = i). These
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	41 represent the probability of observing each symbol in a given state.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	42 - the initial state distribution. This gives the probability of starting
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	43 in each state.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	44
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	45 To ground this discussion, take a common NLP application, part-of-speech (POS)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	46 tagging. An HMM is desirable for this task as the highest probability tag
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	47 sequence can be calculated for a given sequence of word forms. This differs
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	48 from other tagging techniques which often tag each word individually, seeking
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	49 to optimise each individual tagging greedily without regard to the optimal
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	50 combination of tags for a larger unit, such as a sentence. The HMM does this
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	51 with the Viterbi algorithm, which efficiently computes the optimal path
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	52 through the graph given the sequence of words forms.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	53
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	54 In POS tagging the states usually have a 1:1 correspondence with the tag
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	55 alphabet - i.e. each state represents a single tag. The output observation
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	56 alphabet is the set of word forms (the lexicon), and the remaining three
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	57 parameters are derived by a training regime. With this information the
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	58 probability of a given sentence can be easily derived, by simply summing the
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	59 probability of each distinct path through the model. Similarly, the highest
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	60 probability tagging sequence can be derived with the Viterbi algorithm,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	61 yielding a state sequence which can be mapped into a tag sequence.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	62
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	63 This discussion assumes that the HMM has been trained. This is probably the
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	64 most difficult task with the model, and requires either MLE estimates of the
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	65 parameters or unsupervised learning using the Baum-Welch algorithm, a variant
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	66 of EM.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	67
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	68 For more information, please consult the source code for this module,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	69 which includes extensive demonstration code.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	70 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	71 from __future__ import print_function, unicode_literals, division
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	72
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	73 import re
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	74 import itertools
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	75
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	76 try:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	77 import numpy as np
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	78 except ImportError:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	79 pass
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	80
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	81 from nltk.probability import (FreqDist, ConditionalFreqDist,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	82 ConditionalProbDist, DictionaryProbDist,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	83 DictionaryConditionalProbDist,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	84 LidstoneProbDist, MutableProbDist,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	85 MLEProbDist, RandomProbDist)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	86 from nltk.metrics import accuracy
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	87 from nltk.util import LazyMap, unique_list
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	88 from nltk.compat import python_2_unicode_compatible, izip, imap
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	89 from nltk.tag.api import TaggerI
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	90
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	91
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	92 _TEXT = 0 # index of text in a tuple
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	93 _TAG = 1 # index of tag in a tuple
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	94
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	95 def _identity(labeled_symbols):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	96 return labeled_symbols
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	97
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	98 @python_2_unicode_compatible
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	99 class HiddenMarkovModelTagger(TaggerI):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	100 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	101 Hidden Markov model class, a generative model for labelling sequence data.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	102 These models define the joint probability of a sequence of symbols and
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	103 their labels (state transitions) as the product of the starting state
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	104 probability, the probability of each state transition, and the probability
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	105 of each observation being generated from each state. This is described in
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	106 more detail in the module documentation.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	107
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	108 This implementation is based on the HMM description in Chapter 8, Huang,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	109 Acero and Hon, Spoken Language Processing and includes an extension for
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	110 training shallow HMM parsers or specialized HMMs as in Molina et.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	111 al, 2002. A specialized HMM modifies training data by applying a
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	112 specialization function to create a new training set that is more
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	113 appropriate for sequential tagging with an HMM. A typical use case is
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	114 chunking.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	115
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	116 :param symbols: the set of output symbols (alphabet)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	117 :type symbols: seq of any
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	118 :param states: a set of states representing state space
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	119 :type states: seq of any
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	120 :param transitions: transition probabilities; Pr(s_i \| s_j) is the
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	121 probability of transition from state i given the model is in
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	122 state_j
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	123 :type transitions: ConditionalProbDistI
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	124 :param outputs: output probabilities; Pr(o_k \| s_i) is the probability
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	125 of emitting symbol k when entering state i
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	126 :type outputs: ConditionalProbDistI
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	127 :param priors: initial state distribution; Pr(s_i) is the probability
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	128 of starting in state i
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	129 :type priors: ProbDistI
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	130 :param transform: an optional function for transforming training
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	131 instances, defaults to the identity function.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	132 :type transform: callable
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	133 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	134 def __init__(self, symbols, states, transitions, outputs, priors,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	135 transform=_identity):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	136 self._symbols = unique_list(symbols)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	137 self._states = unique_list(states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	138 self._transitions = transitions
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	139 self._outputs = outputs
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	140 self._priors = priors
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	141 self._cache = None
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	142 self._transform = transform
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	143
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	144 @classmethod
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	145 def _train(cls, labeled_sequence, test_sequence=None,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	146 unlabeled_sequence=None, transform=_identity,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	147 estimator=None, **kwargs):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	148
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	149 if estimator is None:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	150 def estimator(fd, bins):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	151 return LidstoneProbDist(fd, 0.1, bins)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	152
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	153 labeled_sequence = LazyMap(transform, labeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	154 symbols = unique_list(word for sent in labeled_sequence
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	155 for word, tag in sent)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	156 tag_set = unique_list(tag for sent in labeled_sequence
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	157 for word, tag in sent)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	158
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	159 trainer = HiddenMarkovModelTrainer(tag_set, symbols)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	160 hmm = trainer.train_supervised(labeled_sequence, estimator=estimator)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	161 hmm = cls(hmm._symbols, hmm._states, hmm._transitions, hmm._outputs,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	162 hmm._priors, transform=transform)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	163
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	164 if test_sequence:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	165 hmm.test(test_sequence, verbose=kwargs.get('verbose', False))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	166
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	167 if unlabeled_sequence:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	168 max_iterations = kwargs.get('max_iterations', 5)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	169 hmm = trainer.train_unsupervised(unlabeled_sequence, model=hmm,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	170 max_iterations=max_iterations)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	171 if test_sequence:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	172 hmm.test(test_sequence, verbose=kwargs.get('verbose', False))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	173
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	174 return hmm
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	175
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	176 @classmethod
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	177 def train(cls, labeled_sequence, test_sequence=None,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	178 unlabeled_sequence=None, **kwargs):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	179 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	180 Train a new HiddenMarkovModelTagger using the given labeled and
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	181 unlabeled training instances. Testing will be performed if test
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	182 instances are provided.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	183
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	184 :return: a hidden markov model tagger
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	185 :rtype: HiddenMarkovModelTagger
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	186 :param labeled_sequence: a sequence of labeled training instances,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	187 i.e. a list of sentences represented as tuples
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	188 :type labeled_sequence: list(list)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	189 :param test_sequence: a sequence of labeled test instances
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	190 :type test_sequence: list(list)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	191 :param unlabeled_sequence: a sequence of unlabeled training instances,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	192 i.e. a list of sentences represented as words
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	193 :type unlabeled_sequence: list(list)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	194 :param transform: an optional function for transforming training
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	195 instances, defaults to the identity function, see ``transform()``
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	196 :type transform: function
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	197 :param estimator: an optional function or class that maps a
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	198 condition's frequency distribution to its probability
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	199 distribution, defaults to a Lidstone distribution with gamma = 0.1
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	200 :type estimator: class or function
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	201 :param verbose: boolean flag indicating whether training should be
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	202 verbose or include printed output
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	203 :type verbose: bool
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	204 :param max_iterations: number of Baum-Welch interations to perform
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	205 :type max_iterations: int
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	206 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	207 return cls._train(labeled_sequence, test_sequence,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	208 unlabeled_sequence, **kwargs)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	209
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	210 def probability(self, sequence):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	211 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	212 Returns the probability of the given symbol sequence. If the sequence
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	213 is labelled, then returns the joint probability of the symbol, state
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	214 sequence. Otherwise, uses the forward algorithm to find the
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	215 probability over all label sequences.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	216
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	217 :return: the probability of the sequence
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	218 :rtype: float
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	219 :param sequence: the sequence of symbols which must contain the TEXT
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	220 property, and optionally the TAG property
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	221 :type sequence: Token
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	222 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	223 return 2**(self.log_probability(self._transform(sequence)))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	224
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	225 def log_probability(self, sequence):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	226 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	227 Returns the log-probability of the given symbol sequence. If the
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	228 sequence is labelled, then returns the joint log-probability of the
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	229 symbol, state sequence. Otherwise, uses the forward algorithm to find
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	230 the log-probability over all label sequences.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	231
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	232 :return: the log-probability of the sequence
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	233 :rtype: float
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	234 :param sequence: the sequence of symbols which must contain the TEXT
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	235 property, and optionally the TAG property
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	236 :type sequence: Token
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	237 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	238 sequence = self._transform(sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	239
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	240 T = len(sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	241
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	242 if T > 0 and sequence[0][_TAG]:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	243 last_state = sequence[0][_TAG]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	244 p = self._priors.logprob(last_state) + \
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	245 self._output_logprob(last_state, sequence[0][_TEXT])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	246 for t in range(1, T):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	247 state = sequence[t][_TAG]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	248 p += self._transitions[last_state].logprob(state) + \
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	249 self._output_logprob(state, sequence[t][_TEXT])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	250 last_state = state
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	251 return p
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	252 else:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	253 alpha = self._forward_probability(sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	254 p = logsumexp2(alpha[T-1])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	255 return p
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	256
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	257 def tag(self, unlabeled_sequence):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	258 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	259 Tags the sequence with the highest probability state sequence. This
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	260 uses the best_path method to find the Viterbi path.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	261
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	262 :return: a labelled sequence of symbols
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	263 :rtype: list
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	264 :param unlabeled_sequence: the sequence of unlabeled symbols
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	265 :type unlabeled_sequence: list
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	266 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	267 unlabeled_sequence = self._transform(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	268 return self._tag(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	269
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	270 def _tag(self, unlabeled_sequence):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	271 path = self._best_path(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	272 return list(izip(unlabeled_sequence, path))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	273
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	274 def _output_logprob(self, state, symbol):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	275 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	276 :return: the log probability of the symbol being observed in the given
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	277 state
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	278 :rtype: float
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	279 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	280 return self._outputs[state].logprob(symbol)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	281
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	282 def _create_cache(self):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	283 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	284 The cache is a tuple (P, O, X, S) where:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	285
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	286 - S maps symbols to integers. I.e., it is the inverse
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	287 mapping from self._symbols; for each symbol s in
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	288 self._symbols, the following is true::
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	289
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	290 self._symbols[S[s]] == s
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	291
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	292 - O is the log output probabilities::
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	293
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	294 O[i,k] = log( P(token[t]=sym[k]\|tag[t]=state[i]) )
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	295
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	296 - X is the log transition probabilities::
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	297
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	298 X[i,j] = log( P(tag[t]=state[j]\|tag[t-1]=state[i]) )
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	299
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	300 - P is the log prior probabilities::
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	301
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	302 P[i] = log( P(tag[0]=state[i]) )
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	303 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	304 if not self._cache:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	305 N = len(self._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	306 M = len(self._symbols)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	307 P = np.zeros(N, np.float32)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	308 X = np.zeros((N, N), np.float32)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	309 O = np.zeros((N, M), np.float32)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	310 for i in range(N):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	311 si = self._states[i]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	312 P[i] = self._priors.logprob(si)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	313 for j in range(N):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	314 X[i, j] = self._transitions[si].logprob(self._states[j])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	315 for k in range(M):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	316 O[i, k] = self._output_logprob(si, self._symbols[k])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	317 S = {}
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	318 for k in range(M):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	319 S[self._symbols[k]] = k
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	320 self._cache = (P, O, X, S)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	321
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	322 def _update_cache(self, symbols):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	323 # add new symbols to the symbol table and repopulate the output
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	324 # probabilities and symbol table mapping
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	325 if symbols:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	326 self._create_cache()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	327 P, O, X, S = self._cache
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	328 for symbol in symbols:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	329 if symbol not in self._symbols:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	330 self._cache = None
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	331 self._symbols.append(symbol)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	332 # don't bother with the work if there aren't any new symbols
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	333 if not self._cache:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	334 N = len(self._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	335 M = len(self._symbols)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	336 Q = O.shape[1]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	337 # add new columns to the output probability table without
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	338 # destroying the old probabilities
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	339 O = np.hstack([O, np.zeros((N, M - Q), np.float32)])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	340 for i in range(N):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	341 si = self._states[i]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	342 # only calculate probabilities for new symbols
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	343 for k in range(Q, M):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	344 O[i, k] = self._output_logprob(si, self._symbols[k])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	345 # only create symbol mappings for new symbols
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	346 for k in range(Q, M):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	347 S[self._symbols[k]] = k
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	348 self._cache = (P, O, X, S)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	349
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	350 def reset_cache(self):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	351 self._cache = None
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	352
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	353 def best_path(self, unlabeled_sequence):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	354 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	355 Returns the state sequence of the optimal (most probable) path through
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	356 the HMM. Uses the Viterbi algorithm to calculate this part by dynamic
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	357 programming.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	358
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	359 :return: the state sequence
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	360 :rtype: sequence of any
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	361 :param unlabeled_sequence: the sequence of unlabeled symbols
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	362 :type unlabeled_sequence: list
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	363 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	364 unlabeled_sequence = self._transform(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	365 return self._best_path(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	366
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	367 def _best_path(self, unlabeled_sequence):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	368 T = len(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	369 N = len(self._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	370 self._create_cache()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	371 self._update_cache(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	372 P, O, X, S = self._cache
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	373
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	374 V = np.zeros((T, N), np.float32)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	375 B = -np.ones((T, N), np.int)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	376
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	377 V[0] = P + O[:, S[unlabeled_sequence[0]]]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	378 for t in range(1, T):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	379 for j in range(N):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	380 vs = V[t-1, :] + X[:, j]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	381 best = np.argmax(vs)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	382 V[t, j] = vs[best] + O[j, S[unlabeled_sequence[t]]]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	383 B[t, j] = best
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	384
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	385 current = np.argmax(V[T-1,:])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	386 sequence = [current]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	387 for t in range(T-1, 0, -1):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	388 last = B[t, current]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	389 sequence.append(last)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	390 current = last
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	391
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	392 sequence.reverse()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	393 return list(map(self._states.__getitem__, sequence))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	394
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	395 def best_path_simple(self, unlabeled_sequence):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	396 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	397 Returns the state sequence of the optimal (most probable) path through
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	398 the HMM. Uses the Viterbi algorithm to calculate this part by dynamic
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	399 programming. This uses a simple, direct method, and is included for
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	400 teaching purposes.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	401
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	402 :return: the state sequence
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	403 :rtype: sequence of any
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	404 :param unlabeled_sequence: the sequence of unlabeled symbols
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	405 :type unlabeled_sequence: list
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	406 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	407 unlabeled_sequence = self._transform(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	408 return self._best_path_simple(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	409
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	410 def _best_path_simple(self, unlabeled_sequence):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	411 T = len(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	412 N = len(self._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	413 V = np.zeros((T, N), np.float64)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	414 B = {}
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	415
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	416 # find the starting log probabilities for each state
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	417 symbol = unlabeled_sequence[0]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	418 for i, state in enumerate(self._states):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	419 V[0, i] = self._priors.logprob(state) + \
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	420 self._output_logprob(state, symbol)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	421 B[0, state] = None
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	422
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	423 # find the maximum log probabilities for reaching each state at time t
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	424 for t in range(1, T):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	425 symbol = unlabeled_sequence[t]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	426 for j in range(N):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	427 sj = self._states[j]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	428 best = None
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	429 for i in range(N):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	430 si = self._states[i]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	431 va = V[t-1, i] + self._transitions[si].logprob(sj)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	432 if not best or va > best[0]:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	433 best = (va, si)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	434 V[t, j] = best[0] + self._output_logprob(sj, symbol)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	435 B[t, sj] = best[1]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	436
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	437 # find the highest probability final state
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	438 best = None
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	439 for i in range(N):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	440 val = V[T-1, i]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	441 if not best or val > best[0]:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	442 best = (val, self._states[i])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	443
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	444 # traverse the back-pointers B to find the state sequence
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	445 current = best[1]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	446 sequence = [current]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	447 for t in range(T-1, 0, -1):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	448 last = B[t, current]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	449 sequence.append(last)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	450 current = last
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	451
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	452 sequence.reverse()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	453 return sequence
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	454
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	455 def random_sample(self, rng, length):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	456 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	457 Randomly sample the HMM to generate a sentence of a given length. This
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	458 samples the prior distribution then the observation distribution and
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	459 transition distribution for each subsequent observation and state.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	460 This will mostly generate unintelligible garbage, but can provide some
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	461 amusement.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	462
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	463 :return: the randomly created state/observation sequence,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	464 generated according to the HMM's probability
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	465 distributions. The SUBTOKENS have TEXT and TAG
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	466 properties containing the observation and state
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	467 respectively.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	468 :rtype: list
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	469 :param rng: random number generator
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	470 :type rng: Random (or any object with a random() method)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	471 :param length: desired output length
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	472 :type length: int
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	473 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	474
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	475 # sample the starting state and symbol prob dists
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	476 tokens = []
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	477 state = self._sample_probdist(self._priors, rng.random(), self._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	478 symbol = self._sample_probdist(self._outputs[state],
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	479 rng.random(), self._symbols)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	480 tokens.append((symbol, state))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	481
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	482 for i in range(1, length):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	483 # sample the state transition and symbol prob dists
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	484 state = self._sample_probdist(self._transitions[state],
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	485 rng.random(), self._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	486 symbol = self._sample_probdist(self._outputs[state],
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	487 rng.random(), self._symbols)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	488 tokens.append((symbol, state))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	489
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	490 return tokens
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	491
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	492 def _sample_probdist(self, probdist, p, samples):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	493 cum_p = 0
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	494 for sample in samples:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	495 add_p = probdist.prob(sample)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	496 if cum_p <= p <= cum_p + add_p:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	497 return sample
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	498 cum_p += add_p
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	499 raise Exception('Invalid probability distribution - '
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	500 'does not sum to one')
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	501
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	502 def entropy(self, unlabeled_sequence):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	503 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	504 Returns the entropy over labellings of the given sequence. This is
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	505 given by::
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	506
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	507 H(O) = - sum_S Pr(S \| O) log Pr(S \| O)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	508
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	509 where the summation ranges over all state sequences, S. Let
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	510 Z = Pr(O) = sum_S Pr(S, O)} where the summation ranges over all state
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	511 sequences and O is the observation sequence. As such the entropy can
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	512 be re-expressed as::
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	513
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	514 H = - sum_S Pr(S \| O) log [ Pr(S, O) / Z ]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	515 = log Z - sum_S Pr(S \| O) log Pr(S, 0)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	516 = log Z - sum_S Pr(S \| O) [ log Pr(S_0) + sum_t Pr(S_t \| S_{t-1}) + sum_t Pr(O_t \| S_t) ]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	517
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	518 The order of summation for the log terms can be flipped, allowing
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	519 dynamic programming to be used to calculate the entropy. Specifically,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	520 we use the forward and backward probabilities (alpha, beta) giving::
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	521
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	522 H = log Z - sum_s0 alpha_0(s0) beta_0(s0) / Z * log Pr(s0)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	523 + sum_t,si,sj alpha_t(si) Pr(sj \| si) Pr(O_t+1 \| sj) beta_t(sj) / Z * log Pr(sj \| si)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	524 + sum_t,st alpha_t(st) beta_t(st) / Z * log Pr(O_t \| st)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	525
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	526 This simply uses alpha and beta to find the probabilities of partial
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	527 sequences, constrained to include the given state(s) at some point in
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	528 time.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	529 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	530 unlabeled_sequence = self._transform(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	531
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	532 T = len(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	533 N = len(self._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	534
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	535 alpha = self._forward_probability(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	536 beta = self._backward_probability(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	537 normalisation = logsumexp2(alpha[T-1])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	538
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	539 entropy = normalisation
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	540
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	541 # starting state, t = 0
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	542 for i, state in enumerate(self._states):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	543 p = 2**(alpha[0, i] + beta[0, i] - normalisation)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	544 entropy -= p * self._priors.logprob(state)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	545 #print 'p(s_0 = %s) =' % state, p
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	546
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	547 # state transitions
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	548 for t0 in range(T - 1):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	549 t1 = t0 + 1
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	550 for i0, s0 in enumerate(self._states):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	551 for i1, s1 in enumerate(self._states):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	552 p = 2**(alpha[t0, i0] + self._transitions[s0].logprob(s1) +
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	553 self._outputs[s1].logprob(
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	554 unlabeled_sequence[t1][_TEXT]) +
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	555 beta[t1, i1] - normalisation)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	556 entropy -= p * self._transitions[s0].logprob(s1)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	557 #print 'p(s_%d = %s, s_%d = %s) =' % (t0, s0, t1, s1), p
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	558
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	559 # symbol emissions
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	560 for t in range(T):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	561 for i, state in enumerate(self._states):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	562 p = 2**(alpha[t, i] + beta[t, i] - normalisation)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	563 entropy -= p * self._outputs[state].logprob(
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	564 unlabeled_sequence[t][_TEXT])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	565 #print 'p(s_%d = %s) =' % (t, state), p
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	566
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	567 return entropy
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	568
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	569 def point_entropy(self, unlabeled_sequence):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	570 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	571 Returns the pointwise entropy over the possible states at each
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	572 position in the chain, given the observation sequence.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	573 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	574 unlabeled_sequence = self._transform(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	575
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	576 T = len(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	577 N = len(self._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	578
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	579 alpha = self._forward_probability(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	580 beta = self._backward_probability(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	581 normalisation = logsumexp2(alpha[T-1])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	582
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	583 entropies = np.zeros(T, np.float64)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	584 probs = np.zeros(N, np.float64)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	585 for t in range(T):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	586 for s in range(N):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	587 probs[s] = alpha[t, s] + beta[t, s] - normalisation
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	588
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	589 for s in range(N):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	590 entropies[t] -= 2*(probs[s]) probs[s]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	591
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	592 return entropies
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	593
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	594 def _exhaustive_entropy(self, unlabeled_sequence):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	595 unlabeled_sequence = self._transform(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	596
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	597 T = len(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	598 N = len(self._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	599
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	600 labellings = [[state] for state in self._states]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	601 for t in range(T - 1):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	602 current = labellings
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	603 labellings = []
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	604 for labelling in current:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	605 for state in self._states:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	606 labellings.append(labelling + [state])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	607
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	608 log_probs = []
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	609 for labelling in labellings:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	610 labeled_sequence = unlabeled_sequence[:]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	611 for t, label in enumerate(labelling):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	612 labeled_sequence[t] = (labeled_sequence[t][_TEXT], label)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	613 lp = self.log_probability(labeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	614 log_probs.append(lp)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	615 normalisation = _log_add(*log_probs)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	616
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	617 #ps = zeros((T, N), float64)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	618 #for labelling, lp in zip(labellings, log_probs):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	619 #for t in range(T):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	620 #ps[t, self._states.index(labelling[t])] += \
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	621 # 2**(lp - normalisation)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	622
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	623 #for t in range(T):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	624 #print 'prob[%d] =' % t, ps[t]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	625
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	626 entropy = 0
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	627 for lp in log_probs:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	628 lp -= normalisation
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	629 entropy -= 2*(lp) lp
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	630
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	631 return entropy
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	632
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	633 def _exhaustive_point_entropy(self, unlabeled_sequence):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	634 unlabeled_sequence = self._transform(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	635
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	636 T = len(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	637 N = len(self._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	638
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	639 labellings = [[state] for state in self._states]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	640 for t in range(T - 1):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	641 current = labellings
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	642 labellings = []
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	643 for labelling in current:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	644 for state in self._states:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	645 labellings.append(labelling + [state])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	646
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	647 log_probs = []
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	648 for labelling in labellings:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	649 labelled_sequence = unlabeled_sequence[:]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	650 for t, label in enumerate(labelling):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	651 labelled_sequence[t] = (labelled_sequence[t][_TEXT], label)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	652 lp = self.log_probability(labelled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	653 log_probs.append(lp)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	654
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	655 normalisation = _log_add(*log_probs)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	656
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	657 probabilities = _ninf_array((T,N))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	658
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	659 for labelling, lp in zip(labellings, log_probs):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	660 lp -= normalisation
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	661 for t, label in enumerate(labelling):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	662 index = self._states.index(label)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	663 probabilities[t, index] = _log_add(probabilities[t, index], lp)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	664
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	665 entropies = np.zeros(T, np.float64)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	666 for t in range(T):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	667 for s in range(N):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	668 entropies[t] -= 2*(probabilities[t, s]) probabilities[t, s]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	669
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	670 return entropies
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	671
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	672 def _transitions_matrix(self):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	673 """ Return a matrix of transition log probabilities. """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	674 trans_iter = (self._transitions[sj].logprob(si)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	675 for sj in self._states
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	676 for si in self._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	677
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	678 transitions_logprob = np.fromiter(trans_iter, dtype=np.float64)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	679 N = len(self._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	680 return transitions_logprob.reshape((N, N)).T
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	681
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	682 def _outputs_vector(self, symbol):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	683 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	684 Return a vector with log probabilities of emitting a symbol
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	685 when entering states.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	686 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	687 out_iter = (self._output_logprob(sj, symbol) for sj in self._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	688 return np.fromiter(out_iter, dtype=np.float64)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	689
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	690 def _forward_probability(self, unlabeled_sequence):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	691 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	692 Return the forward probability matrix, a T by N array of
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	693 log-probabilities, where T is the length of the sequence and N is the
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	694 number of states. Each entry (t, s) gives the probability of being in
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	695 state s at time t after observing the partial symbol sequence up to
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	696 and including t.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	697
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	698 :param unlabeled_sequence: the sequence of unlabeled symbols
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	699 :type unlabeled_sequence: list
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	700 :return: the forward log probability matrix
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	701 :rtype: array
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	702 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	703 T = len(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	704 N = len(self._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	705 alpha = _ninf_array((T, N))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	706
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	707 transitions_logprob = self._transitions_matrix()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	708
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	709 # Initialization
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	710 symbol = unlabeled_sequence[0][_TEXT]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	711 for i, state in enumerate(self._states):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	712 alpha[0, i] = self._priors.logprob(state) + \
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	713 self._output_logprob(state, symbol)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	714
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	715 # Induction
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	716 for t in range(1, T):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	717 symbol = unlabeled_sequence[t][_TEXT]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	718 output_logprob = self._outputs_vector(symbol)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	719
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	720 for i in range(N):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	721 summand = alpha[t-1] + transitions_logprob[i]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	722 alpha[t, i] = logsumexp2(summand) + output_logprob[i]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	723
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	724 return alpha
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	725
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	726 def _backward_probability(self, unlabeled_sequence):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	727 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	728 Return the backward probability matrix, a T by N array of
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	729 log-probabilities, where T is the length of the sequence and N is the
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	730 number of states. Each entry (t, s) gives the probability of being in
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	731 state s at time t after observing the partial symbol sequence from t
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	732 .. T.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	733
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	734 :return: the backward log probability matrix
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	735 :rtype: array
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	736 :param unlabeled_sequence: the sequence of unlabeled symbols
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	737 :type unlabeled_sequence: list
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	738 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	739 T = len(unlabeled_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	740 N = len(self._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	741 beta = _ninf_array((T, N))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	742
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	743 transitions_logprob = self._transitions_matrix().T
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	744
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	745 # initialise the backward values;
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	746 # "1" is an arbitrarily chosen value from Rabiner tutorial
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	747 beta[T-1, :] = np.log2(1)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	748
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	749 # inductively calculate remaining backward values
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	750 for t in range(T-2, -1, -1):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	751 symbol = unlabeled_sequence[t+1][_TEXT]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	752 outputs = self._outputs_vector(symbol)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	753
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	754 for i in range(N):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	755 summand = transitions_logprob[i] + beta[t+1] + outputs
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	756 beta[t, i] = logsumexp2(summand)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	757
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	758 return beta
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	759
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	760 def test(self, test_sequence, verbose=False, **kwargs):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	761 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	762 Tests the HiddenMarkovModelTagger instance.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	763
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	764 :param test_sequence: a sequence of labeled test instances
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	765 :type test_sequence: list(list)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	766 :param verbose: boolean flag indicating whether training should be
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	767 verbose or include printed output
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	768 :type verbose: bool
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	769 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	770
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	771 def words(sent):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	772 return [word for (word, tag) in sent]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	773
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	774 def tags(sent):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	775 return [tag for (word, tag) in sent]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	776
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	777 def flatten(seq):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	778 return list(itertools.chain(*seq))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	779
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	780 test_sequence = self._transform(test_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	781 predicted_sequence = list(imap(self._tag, imap(words, test_sequence)))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	782
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	783 if verbose:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	784 for test_sent, predicted_sent in izip(test_sequence, predicted_sequence):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	785 print('Test:',
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	786 ' '.join('%s/%s' % (token, tag)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	787 for (token, tag) in test_sent))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	788 print()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	789 print('Untagged:',
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	790 ' '.join("%s" % token for (token, tag) in test_sent))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	791 print()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	792 print('HMM-tagged:',
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	793 ' '.join('%s/%s' % (token, tag)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	794 for (token, tag) in predicted_sent))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	795 print()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	796 print('Entropy:',
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	797 self.entropy([(token, None) for
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	798 (token, tag) in predicted_sent]))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	799 print()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	800 print('-' * 60)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	801
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	802 test_tags = flatten(imap(tags, test_sequence))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	803 predicted_tags = flatten(imap(tags, predicted_sequence))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	804
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	805 acc = accuracy(test_tags, predicted_tags)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	806 count = sum(len(sent) for sent in test_sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	807 print('accuracy over %d tokens: %.2f' % (count, acc * 100))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	808
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	809 def __repr__(self):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	810 return ('<HiddenMarkovModelTagger %d states and %d output symbols>'
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	811 % (len(self._states), len(self._symbols)))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	812
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	813
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	814 class HiddenMarkovModelTrainer(object):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	815 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	816 Algorithms for learning HMM parameters from training data. These include
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	817 both supervised learning (MLE) and unsupervised learning (Baum-Welch).
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	818
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	819 Creates an HMM trainer to induce an HMM with the given states and
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	820 output symbol alphabet. A supervised and unsupervised training
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	821 method may be used. If either of the states or symbols are not given,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	822 these may be derived from supervised training.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	823
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	824 :param states: the set of state labels
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	825 :type states: sequence of any
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	826 :param symbols: the set of observation symbols
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	827 :type symbols: sequence of any
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	828 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	829 def __init__(self, states=None, symbols=None):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	830 self._states = (states if states else [])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	831 self._symbols = (symbols if symbols else [])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	832
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	833 def train(self, labeled_sequences=None, unlabeled_sequences=None,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	834 **kwargs):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	835 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	836 Trains the HMM using both (or either of) supervised and unsupervised
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	837 techniques.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	838
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	839 :return: the trained model
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	840 :rtype: HiddenMarkovModelTagger
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	841 :param labelled_sequences: the supervised training data, a set of
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	842 labelled sequences of observations
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	843 :type labelled_sequences: list
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	844 :param unlabeled_sequences: the unsupervised training data, a set of
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	845 sequences of observations
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	846 :type unlabeled_sequences: list
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	847 :param kwargs: additional arguments to pass to the training methods
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	848 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	849 assert labeled_sequences or unlabeled_sequences
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	850 model = None
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	851 if labeled_sequences:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	852 model = self.train_supervised(labeled_sequences, **kwargs)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	853 if unlabeled_sequences:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	854 if model: kwargs['model'] = model
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	855 model = self.train_unsupervised(unlabeled_sequences, **kwargs)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	856 return model
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	857
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	858
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	859 def _baum_welch_step(self, sequence, model, symbol_to_number):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	860 N = len(model._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	861 M = len(model._symbols)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	862 T = len(sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	863
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	864 # compute forward and backward probabilities
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	865 alpha = model._forward_probability(sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	866 beta = model._backward_probability(sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	867
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	868 # find the log probability of the sequence
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	869 lpk = logsumexp2(alpha[T-1])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	870
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	871 A_numer = _ninf_array((N, N))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	872 B_numer = _ninf_array((N, M))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	873 A_denom = _ninf_array(N)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	874 B_denom = _ninf_array(N)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	875
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	876 transitions_logprob = model._transitions_matrix().T
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	877
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	878 for t in range(T):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	879 symbol = sequence[t][_TEXT] # not found? FIXME
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	880 next_symbol = None
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	881 if t < T - 1:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	882 next_symbol = sequence[t+1][_TEXT] # not found? FIXME
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	883 xi = symbol_to_number[symbol]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	884
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	885 next_outputs_logprob = model._outputs_vector(next_symbol)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	886 alpha_plus_beta = alpha[t] + beta[t]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	887
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	888 if t < T - 1:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	889 numer_add = transitions_logprob + next_outputs_logprob + \
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	890 beta[t+1] + alpha[t].reshape(N, 1)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	891 A_numer = np.logaddexp2(A_numer, numer_add)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	892 A_denom = np.logaddexp2(A_denom, alpha_plus_beta)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	893 else:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	894 B_denom = np.logaddexp2(A_denom, alpha_plus_beta)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	895
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	896 B_numer[:,xi] = np.logaddexp2(B_numer[:,xi], alpha_plus_beta)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	897
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	898 return lpk, A_numer, A_denom, B_numer, B_denom
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	899
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	900 def train_unsupervised(self, unlabeled_sequences, update_outputs=True,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	901 **kwargs):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	902 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	903 Trains the HMM using the Baum-Welch algorithm to maximise the
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	904 probability of the data sequence. This is a variant of the EM
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	905 algorithm, and is unsupervised in that it doesn't need the state
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	906 sequences for the symbols. The code is based on 'A Tutorial on Hidden
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	907 Markov Models and Selected Applications in Speech Recognition',
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	908 Lawrence Rabiner, IEEE, 1989.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	909
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	910 :return: the trained model
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	911 :rtype: HiddenMarkovModelTagger
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	912 :param unlabeled_sequences: the training data, a set of
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	913 sequences of observations
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	914 :type unlabeled_sequences: list
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	915
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	916 kwargs may include following parameters:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	917
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	918 :param model: a HiddenMarkovModelTagger instance used to begin
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	919 the Baum-Welch algorithm
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	920 :param max_iterations: the maximum number of EM iterations
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	921 :param convergence_logprob: the maximum change in log probability to
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	922 allow convergence
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	923 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	924
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	925 # create a uniform HMM, which will be iteratively refined, unless
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	926 # given an existing model
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	927 model = kwargs.get('model')
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	928 if not model:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	929 priors = RandomProbDist(self._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	930 transitions = DictionaryConditionalProbDist(
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	931 dict((state, RandomProbDist(self._states))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	932 for state in self._states))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	933 outputs = DictionaryConditionalProbDist(
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	934 dict((state, RandomProbDist(self._symbols))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	935 for state in self._states))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	936 model = HiddenMarkovModelTagger(self._symbols, self._states,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	937 transitions, outputs, priors)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	938
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	939 self._states = model._states
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	940 self._symbols = model._symbols
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	941
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	942 N = len(self._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	943 M = len(self._symbols)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	944 symbol_numbers = dict((sym, i) for i, sym in enumerate(self._symbols))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	945
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	946 # update model prob dists so that they can be modified
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	947 # model._priors = MutableProbDist(model._priors, self._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	948
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	949 model._transitions = DictionaryConditionalProbDist(
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	950 dict((s, MutableProbDist(model._transitions[s], self._states))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	951 for s in self._states))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	952
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	953 if update_outputs:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	954 model._outputs = DictionaryConditionalProbDist(
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	955 dict((s, MutableProbDist(model._outputs[s], self._symbols))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	956 for s in self._states))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	957
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	958 model.reset_cache()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	959
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	960 # iterate until convergence
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	961 converged = False
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	962 last_logprob = None
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	963 iteration = 0
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	964 max_iterations = kwargs.get('max_iterations', 1000)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	965 epsilon = kwargs.get('convergence_logprob', 1e-6)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	966
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	967 while not converged and iteration < max_iterations:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	968 A_numer = _ninf_array((N, N))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	969 B_numer = _ninf_array((N, M))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	970 A_denom = _ninf_array(N)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	971 B_denom = _ninf_array(N)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	972
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	973 logprob = 0
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	974 for sequence in unlabeled_sequences:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	975 sequence = list(sequence)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	976 if not sequence:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	977 continue
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	978
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	979 (lpk, seq_A_numer, seq_A_denom,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	980 seq_B_numer, seq_B_denom) = self._baum_welch_step(sequence, model, symbol_numbers)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	981
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	982 # add these sums to the global A and B values
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	983 for i in range(N):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	984 A_numer[i] = np.logaddexp2(A_numer[i], seq_A_numer[i]-lpk)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	985 B_numer[i] = np.logaddexp2(B_numer[i], seq_B_numer[i]-lpk)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	986
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	987 A_denom = np.logaddexp2(A_denom, seq_A_denom-lpk)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	988 B_denom = np.logaddexp2(B_denom, seq_B_denom-lpk)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	989
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	990 logprob += lpk
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	991
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	992 # use the calculated values to update the transition and output
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	993 # probability values
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	994 for i in range(N):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	995 logprob_Ai = A_numer[i] - A_denom[i]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	996 logprob_Bi = B_numer[i] - B_denom[i]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	997
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	998 # We should normalize all probabilities (see p.391 Huang et al)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	999 # Let sum(P) be K.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1000 # We can divide each Pi by K to make sum(P) == 1.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1001 # Pi' = Pi/K
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1002 # log2(Pi') = log2(Pi) - log2(K)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1003 logprob_Ai -= logsumexp2(logprob_Ai)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1004 logprob_Bi -= logsumexp2(logprob_Bi)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1005
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1006 # update output and transition probabilities
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1007 si = self._states[i]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1008
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1009 for j in range(N):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1010 sj = self._states[j]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1011 model._transitions[si].update(sj, logprob_Ai[j])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1012
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1013 if update_outputs:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1014 for k in range(M):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1015 ok = self._symbols[k]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1016 model._outputs[si].update(ok, logprob_Bi[k])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1017
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1018 # Rabiner says the priors don't need to be updated. I don't
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1019 # believe him. FIXME
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1020
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1021 # test for convergence
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1022 if iteration > 0 and abs(logprob - last_logprob) < epsilon:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1023 converged = True
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1024
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1025 print('iteration', iteration, 'logprob', logprob)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1026 iteration += 1
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1027 last_logprob = logprob
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1028
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1029 return model
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1030
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1031 def train_supervised(self, labelled_sequences, estimator=None):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1032 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1033 Supervised training maximising the joint probability of the symbol and
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1034 state sequences. This is done via collecting frequencies of
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1035 transitions between states, symbol observations while within each
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1036 state and which states start a sentence. These frequency distributions
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1037 are then normalised into probability estimates, which can be
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1038 smoothed if desired.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1039
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1040 :return: the trained model
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1041 :rtype: HiddenMarkovModelTagger
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1042 :param labelled_sequences: the training data, a set of
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1043 labelled sequences of observations
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1044 :type labelled_sequences: list
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1045 :param estimator: a function taking
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1046 a FreqDist and a number of bins and returning a CProbDistI;
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1047 otherwise a MLE estimate is used
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1048 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1049
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1050 # default to the MLE estimate
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1051 if estimator is None:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1052 estimator = lambda fdist, bins: MLEProbDist(fdist)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1053
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1054 # count occurrences of starting states, transitions out of each state
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1055 # and output symbols observed in each state
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1056 known_symbols = set(self._symbols)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1057 known_states = set(self._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1058
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1059 starting = FreqDist()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1060 transitions = ConditionalFreqDist()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1061 outputs = ConditionalFreqDist()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1062 for sequence in labelled_sequences:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1063 lasts = None
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1064 for token in sequence:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1065 state = token[_TAG]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1066 symbol = token[_TEXT]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1067 if lasts is None:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1068 starting[state] += 1
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1069 else:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1070 transitions[lasts][state] += 1
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1071 outputs[state][symbol] += 1
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1072 lasts = state
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1073
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1074 # update the state and symbol lists
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1075 if state not in known_states:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1076 self._states.append(state)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1077 known_states.add(state)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1078
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1079 if symbol not in known_symbols:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1080 self._symbols.append(symbol)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1081 known_symbols.add(symbol)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1082
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1083 # create probability distributions (with smoothing)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1084 N = len(self._states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1085 pi = estimator(starting, N)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1086 A = ConditionalProbDist(transitions, estimator, N)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1087 B = ConditionalProbDist(outputs, estimator, len(self._symbols))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1088
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1089 return HiddenMarkovModelTagger(self._symbols, self._states, A, B, pi)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1090
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1091
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1092 def _ninf_array(shape):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1093 res = np.empty(shape, np.float64)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1094 res.fill(-np.inf)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1095 return res
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1096
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1097
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1098 def logsumexp2(arr):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1099 max_ = arr.max()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1100 return np.log2(np.sum(2**(arr - max_))) + max_
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1101
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1102
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1103 def _log_add(*values):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1104 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1105 Adds the logged values, returning the logarithm of the addition.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1106 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1107 x = max(values)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1108 if x > -np.inf:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1109 sum_diffs = 0
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1110 for value in values:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1111 sum_diffs += 2**(value - x)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1112 return x + np.log2(sum_diffs)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1113 else:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1114 return x
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1115
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1116
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1117 def _create_hmm_tagger(states, symbols, A, B, pi):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1118 def pd(values, samples):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1119 d = dict(zip(samples, values))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1120 return DictionaryProbDist(d)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1121
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1122 def cpd(array, conditions, samples):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1123 d = {}
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1124 for values, condition in zip(array, conditions):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1125 d[condition] = pd(values, samples)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1126 return DictionaryConditionalProbDist(d)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1127
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1128 A = cpd(A, states, states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1129 B = cpd(B, states, symbols)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1130 pi = pd(pi, states)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1131 return HiddenMarkovModelTagger(symbols=symbols, states=states,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1132 transitions=A, outputs=B, priors=pi)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1133
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1134
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1135 def _market_hmm_example():
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1136 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1137 Return an example HMM (described at page 381, Huang et al)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1138 """
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1139 states = ['bull', 'bear', 'static']
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1140 symbols = ['up', 'down', 'unchanged']
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1141 A = np.array([[0.6, 0.2, 0.2], [0.5, 0.3, 0.2], [0.4, 0.1, 0.5]], np.float64)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1142 B = np.array([[0.7, 0.1, 0.2], [0.1, 0.6, 0.3], [0.3, 0.3, 0.4]], np.float64)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1143 pi = np.array([0.5, 0.2, 0.3], np.float64)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1144
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1145 model = _create_hmm_tagger(states, symbols, A, B, pi)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1146 return model, states, symbols
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1147
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1148
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1149 def demo():
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1150 # demonstrates HMM probability calculation
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1151
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1152 print()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1153 print("HMM probability calculation demo")
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1154 print()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1155
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1156 model, states, symbols = _market_hmm_example()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1157
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1158 print('Testing', model)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1159
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1160 for test in [['up', 'up'], ['up', 'down', 'up'],
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1161 ['down'] * 5, ['unchanged'] * 5 + ['up']]:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1162
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1163 sequence = [(t, None) for t in test]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1164
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1165 print('Testing with state sequence', test)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1166 print('probability =', model.probability(sequence))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1167 print('tagging = ', model.tag([word for (word,tag) in sequence]))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1168 print('p(tagged) = ', model.probability(sequence))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1169 print('H = ', model.entropy(sequence))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1170 print('H_exh = ', model._exhaustive_entropy(sequence))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1171 print('H(point) = ', model.point_entropy(sequence))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1172 print('H_exh(point)=', model._exhaustive_point_entropy(sequence))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1173 print()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1174
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1175 def load_pos(num_sents):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1176 from nltk.corpus import brown
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1177
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1178 sentences = brown.tagged_sents(categories='news')[:num_sents]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1179
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1180 tag_re = re.compile(r'[]\|--\|[^+-]+')
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1181 tag_set = set()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1182 symbols = set()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1183
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1184 cleaned_sentences = []
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1185 for sentence in sentences:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1186 for i in range(len(sentence)):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1187 word, tag = sentence[i]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1188 word = word.lower() # normalize
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1189 symbols.add(word) # log this word
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1190 # Clean up the tag.
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1191 tag = tag_re.match(tag).group()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1192 tag_set.add(tag)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1193 sentence[i] = (word, tag) # store cleaned-up tagged token
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1194 cleaned_sentences += [sentence]
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1195
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1196 return cleaned_sentences, list(tag_set), list(symbols)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1197
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1198 def demo_pos():
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1199 # demonstrates POS tagging using supervised training
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1200
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1201 print()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1202 print("HMM POS tagging demo")
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1203 print()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1204
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1205 print('Training HMM...')
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1206 labelled_sequences, tag_set, symbols = load_pos(20000)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1207 trainer = HiddenMarkovModelTrainer(tag_set, symbols)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1208 hmm = trainer.train_supervised(labelled_sequences[10:],
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1209 estimator=lambda fd, bins: LidstoneProbDist(fd, 0.1, bins))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1210
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1211 print('Testing...')
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1212 hmm.test(labelled_sequences[:10], verbose=True)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1213
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1214 def _untag(sentences):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1215 unlabeled = []
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1216 for sentence in sentences:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1217 unlabeled.append([(token[_TEXT], None) for token in sentence])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1218 return unlabeled
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1219
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1220 def demo_pos_bw(test=10, supervised=20, unsupervised=10, verbose=True,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1221 max_iterations=5):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1222 # demonstrates the Baum-Welch algorithm in POS tagging
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1223
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1224 print()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1225 print("Baum-Welch demo for POS tagging")
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1226 print()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1227
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1228 print('Training HMM (supervised, %d sentences)...' % supervised)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1229
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1230 sentences, tag_set, symbols = load_pos(test + supervised + unsupervised)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1231
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1232 symbols = set()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1233 for sentence in sentences:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1234 for token in sentence:
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1235 symbols.add(token[_TEXT])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1236
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1237 trainer = HiddenMarkovModelTrainer(tag_set, list(symbols))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1238 hmm = trainer.train_supervised(sentences[test:test+supervised],
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1239 estimator=lambda fd, bins: LidstoneProbDist(fd, 0.1, bins))
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1240
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1241 hmm.test(sentences[:test], verbose=verbose)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1242
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1243 print('Training (unsupervised, %d sentences)...' % unsupervised)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1244 # it's rather slow - so only use 10 samples by default
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1245 unlabeled = _untag(sentences[test+supervised:])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1246 hmm = trainer.train_unsupervised(unlabeled, model=hmm,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1247 max_iterations=max_iterations)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1248 hmm.test(sentences[:test], verbose=verbose)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1249
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1250 def demo_bw():
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1251 # demo Baum Welch by generating some sequences and then performing
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1252 # unsupervised training on them
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1253
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1254 print()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1255 print("Baum-Welch demo for market example")
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1256 print()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1257
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1258 model, states, symbols = _market_hmm_example()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1259
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1260 # generate some random sequences
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1261 training = []
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1262 import random
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1263 rng = random.Random()
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1264 rng.seed(0)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1265 for i in range(10):
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1266 item = model.random_sample(rng, 5)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1267 training.append([(i[0], None) for i in item])
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1268
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1269 # train on those examples, starting with the model that generated them
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1270 trainer = HiddenMarkovModelTrainer(states, symbols)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1271 hmm = trainer.train_unsupervised(training, model=model,
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1272 max_iterations=1000)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1273
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1274
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1275 if __name__ == "__main__":
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1276 import doctest
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1277 doctest.testmod(optionflags=doctest.NORMALIZE_WHITESPACE)
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1278
26d9c0308fcf updated/added from ecclerig version Henry S. Thompson <ht@inf.ed.ac.uk> parents: diff changeset	1279

Mercurial > hg > python

annotate hmm/hmm.py @ 69:157f012ffab7 default tip