File size: 7,412 Bytes
8777447
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
# Natural Language Toolkit: Positive Naive Bayes Classifier
#
# Copyright (C) 2012 NLTK Project
# Author: Alessandro Presta <[email protected]>
# URL: <https://www.nltk.org/>
# For license information, see LICENSE.TXT

"""

A variant of the Naive Bayes Classifier that performs binary classification with

partially-labeled training sets. In other words, assume we want to build a classifier

that assigns each example to one of two complementary classes (e.g., male names and

female names).

If we have a training set with labeled examples for both classes, we can use a

standard Naive Bayes Classifier. However, consider the case when we only have labeled

examples for one of the classes, and other, unlabeled, examples.

Then, assuming a prior distribution on the two labels, we can use the unlabeled set

to estimate the frequencies of the various features.



Let the two possible labels be 1 and 0, and let's say we only have examples labeled 1

and unlabeled examples. We are also given an estimate of P(1).



We compute P(feature|1) exactly as in the standard case.



To compute P(feature|0), we first estimate P(feature) from the unlabeled set (we are

assuming that the unlabeled examples are drawn according to the given prior distribution)

and then express the conditional probability as:



|                  P(feature) - P(feature|1) * P(1)

|  P(feature|0) = ----------------------------------

|                               P(0)



Example:



    >>> from nltk.classify import PositiveNaiveBayesClassifier



Some sentences about sports:



    >>> sports_sentences = [ 'The team dominated the game',

    ...                      'They lost the ball',

    ...                      'The game was intense',

    ...                      'The goalkeeper catched the ball',

    ...                      'The other team controlled the ball' ]



Mixed topics, including sports:



    >>> various_sentences = [ 'The President did not comment',

    ...                       'I lost the keys',

    ...                       'The team won the game',

    ...                       'Sara has two kids',

    ...                       'The ball went off the court',

    ...                       'They had the ball for the whole game',

    ...                       'The show is over' ]



The features of a sentence are simply the words it contains:



    >>> def features(sentence):

    ...     words = sentence.lower().split()

    ...     return dict(('contains(%s)' % w, True) for w in words)



We use the sports sentences as positive examples, the mixed ones ad unlabeled examples:



    >>> positive_featuresets = map(features, sports_sentences)

    >>> unlabeled_featuresets = map(features, various_sentences)

    >>> classifier = PositiveNaiveBayesClassifier.train(positive_featuresets,

    ...                                                 unlabeled_featuresets)



Is the following sentence about sports?



    >>> classifier.classify(features('The cat is on the table'))

    False



What about this one?



    >>> classifier.classify(features('My team lost the game'))

    True

"""

from collections import defaultdict

from nltk.classify.naivebayes import NaiveBayesClassifier
from nltk.probability import DictionaryProbDist, ELEProbDist, FreqDist

##//////////////////////////////////////////////////////
##  Positive Naive Bayes Classifier
##//////////////////////////////////////////////////////


class PositiveNaiveBayesClassifier(NaiveBayesClassifier):
    @staticmethod
    def train(

        positive_featuresets,

        unlabeled_featuresets,

        positive_prob_prior=0.5,

        estimator=ELEProbDist,

    ):
        """

        :param positive_featuresets: An iterable of featuresets that are known as positive

            examples (i.e., their label is ``True``).



        :param unlabeled_featuresets: An iterable of featuresets whose label is unknown.



        :param positive_prob_prior: A prior estimate of the probability of the label

            ``True`` (default 0.5).

        """
        positive_feature_freqdist = defaultdict(FreqDist)
        unlabeled_feature_freqdist = defaultdict(FreqDist)
        feature_values = defaultdict(set)
        fnames = set()

        # Count up how many times each feature value occurred in positive examples.
        num_positive_examples = 0
        for featureset in positive_featuresets:
            for fname, fval in featureset.items():
                positive_feature_freqdist[fname][fval] += 1
                feature_values[fname].add(fval)
                fnames.add(fname)
            num_positive_examples += 1

        # Count up how many times each feature value occurred in unlabeled examples.
        num_unlabeled_examples = 0
        for featureset in unlabeled_featuresets:
            for fname, fval in featureset.items():
                unlabeled_feature_freqdist[fname][fval] += 1
                feature_values[fname].add(fval)
                fnames.add(fname)
            num_unlabeled_examples += 1

        # If a feature didn't have a value given for an instance, then we assume that
        # it gets the implicit value 'None'.
        for fname in fnames:
            count = positive_feature_freqdist[fname].N()
            positive_feature_freqdist[fname][None] += num_positive_examples - count
            feature_values[fname].add(None)

        for fname in fnames:
            count = unlabeled_feature_freqdist[fname].N()
            unlabeled_feature_freqdist[fname][None] += num_unlabeled_examples - count
            feature_values[fname].add(None)

        negative_prob_prior = 1.0 - positive_prob_prior

        # Create the P(label) distribution.
        label_probdist = DictionaryProbDist(
            {True: positive_prob_prior, False: negative_prob_prior}
        )

        # Create the P(fval|label, fname) distribution.
        feature_probdist = {}
        for fname, freqdist in positive_feature_freqdist.items():
            probdist = estimator(freqdist, bins=len(feature_values[fname]))
            feature_probdist[True, fname] = probdist

        for fname, freqdist in unlabeled_feature_freqdist.items():
            global_probdist = estimator(freqdist, bins=len(feature_values[fname]))
            negative_feature_probs = {}
            for fval in feature_values[fname]:
                prob = (
                    global_probdist.prob(fval)
                    - positive_prob_prior * feature_probdist[True, fname].prob(fval)
                ) / negative_prob_prior
                # TODO: We need to add some kind of smoothing here, instead of
                # setting negative probabilities to zero and normalizing.
                negative_feature_probs[fval] = max(prob, 0.0)
            feature_probdist[False, fname] = DictionaryProbDist(
                negative_feature_probs, normalize=True
            )

        return PositiveNaiveBayesClassifier(label_probdist, feature_probdist)


##//////////////////////////////////////////////////////
##  Demo
##//////////////////////////////////////////////////////


def demo():
    from nltk.classify.util import partial_names_demo

    classifier = partial_names_demo(PositiveNaiveBayesClassifier.train)
    classifier.show_most_informative_features()