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Iliyan Angelov
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# Natural Language Toolkit: Positive Naive Bayes Classifier
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#
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# Copyright (C) 2012 NLTK Project
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# Author: Alessandro Presta <alessandro.presta@gmail.com>
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# URL: <https://www.nltk.org/>
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# For license information, see LICENSE.TXT
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"""
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A variant of the Naive Bayes Classifier that performs binary classification with
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partially-labeled training sets. In other words, assume we want to build a classifier
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that assigns each example to one of two complementary classes (e.g., male names and
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female names).
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If we have a training set with labeled examples for both classes, we can use a
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standard Naive Bayes Classifier. However, consider the case when we only have labeled
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examples for one of the classes, and other, unlabeled, examples.
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Then, assuming a prior distribution on the two labels, we can use the unlabeled set
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to estimate the frequencies of the various features.
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Let the two possible labels be 1 and 0, and let's say we only have examples labeled 1
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and unlabeled examples. We are also given an estimate of P(1).
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We compute P(feature|1) exactly as in the standard case.
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To compute P(feature|0), we first estimate P(feature) from the unlabeled set (we are
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assuming that the unlabeled examples are drawn according to the given prior distribution)
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and then express the conditional probability as:
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| P(feature) - P(feature|1) * P(1)
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| P(feature|0) = ----------------------------------
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| P(0)
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Example:
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>>> from nltk.classify import PositiveNaiveBayesClassifier
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Some sentences about sports:
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>>> sports_sentences = [ 'The team dominated the game',
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... 'They lost the ball',
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... 'The game was intense',
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... 'The goalkeeper catched the ball',
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... 'The other team controlled the ball' ]
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Mixed topics, including sports:
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>>> various_sentences = [ 'The President did not comment',
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... 'I lost the keys',
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... 'The team won the game',
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... 'Sara has two kids',
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... 'The ball went off the court',
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... 'They had the ball for the whole game',
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... 'The show is over' ]
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The features of a sentence are simply the words it contains:
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>>> def features(sentence):
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... words = sentence.lower().split()
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... return dict(('contains(%s)' % w, True) for w in words)
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We use the sports sentences as positive examples, the mixed ones ad unlabeled examples:
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>>> positive_featuresets = map(features, sports_sentences)
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>>> unlabeled_featuresets = map(features, various_sentences)
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>>> classifier = PositiveNaiveBayesClassifier.train(positive_featuresets,
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... unlabeled_featuresets)
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Is the following sentence about sports?
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>>> classifier.classify(features('The cat is on the table'))
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False
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What about this one?
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>>> classifier.classify(features('My team lost the game'))
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True
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"""
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from collections import defaultdict
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from nltk.classify.naivebayes import NaiveBayesClassifier
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from nltk.probability import DictionaryProbDist, ELEProbDist, FreqDist
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##//////////////////////////////////////////////////////
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## Positive Naive Bayes Classifier
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##//////////////////////////////////////////////////////
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class PositiveNaiveBayesClassifier(NaiveBayesClassifier):
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@staticmethod
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def train(
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positive_featuresets,
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unlabeled_featuresets,
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positive_prob_prior=0.5,
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estimator=ELEProbDist,
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):
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"""
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:param positive_featuresets: An iterable of featuresets that are known as positive
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examples (i.e., their label is ``True``).
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:param unlabeled_featuresets: An iterable of featuresets whose label is unknown.
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:param positive_prob_prior: A prior estimate of the probability of the label
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``True`` (default 0.5).
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"""
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positive_feature_freqdist = defaultdict(FreqDist)
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unlabeled_feature_freqdist = defaultdict(FreqDist)
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feature_values = defaultdict(set)
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fnames = set()
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# Count up how many times each feature value occurred in positive examples.
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num_positive_examples = 0
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for featureset in positive_featuresets:
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for fname, fval in featureset.items():
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positive_feature_freqdist[fname][fval] += 1
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feature_values[fname].add(fval)
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fnames.add(fname)
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num_positive_examples += 1
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# Count up how many times each feature value occurred in unlabeled examples.
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num_unlabeled_examples = 0
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for featureset in unlabeled_featuresets:
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for fname, fval in featureset.items():
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unlabeled_feature_freqdist[fname][fval] += 1
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feature_values[fname].add(fval)
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fnames.add(fname)
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num_unlabeled_examples += 1
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# If a feature didn't have a value given for an instance, then we assume that
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# it gets the implicit value 'None'.
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for fname in fnames:
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count = positive_feature_freqdist[fname].N()
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positive_feature_freqdist[fname][None] += num_positive_examples - count
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feature_values[fname].add(None)
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for fname in fnames:
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count = unlabeled_feature_freqdist[fname].N()
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unlabeled_feature_freqdist[fname][None] += num_unlabeled_examples - count
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feature_values[fname].add(None)
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negative_prob_prior = 1.0 - positive_prob_prior
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# Create the P(label) distribution.
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label_probdist = DictionaryProbDist(
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{True: positive_prob_prior, False: negative_prob_prior}
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)
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# Create the P(fval|label, fname) distribution.
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feature_probdist = {}
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for fname, freqdist in positive_feature_freqdist.items():
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probdist = estimator(freqdist, bins=len(feature_values[fname]))
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feature_probdist[True, fname] = probdist
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for fname, freqdist in unlabeled_feature_freqdist.items():
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global_probdist = estimator(freqdist, bins=len(feature_values[fname]))
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negative_feature_probs = {}
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for fval in feature_values[fname]:
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prob = (
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global_probdist.prob(fval)
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- positive_prob_prior * feature_probdist[True, fname].prob(fval)
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) / negative_prob_prior
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# TODO: We need to add some kind of smoothing here, instead of
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# setting negative probabilities to zero and normalizing.
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negative_feature_probs[fval] = max(prob, 0.0)
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feature_probdist[False, fname] = DictionaryProbDist(
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negative_feature_probs, normalize=True
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)
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return PositiveNaiveBayesClassifier(label_probdist, feature_probdist)
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##//////////////////////////////////////////////////////
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## Demo
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##//////////////////////////////////////////////////////
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def demo():
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from nltk.classify.util import partial_names_demo
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classifier = partial_names_demo(PositiveNaiveBayesClassifier.train)
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classifier.show_most_informative_features()
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