# Source code for nltk.classify.positivenaivebayes

```# Natural Language Toolkit: Positive Naive Bayes Classifier
#
# Copyright (C) 2012 NLTK Project
# Author: Alessandro Presta <alessandro.presta@gmail.com>
# URL: <https://www.nltk.org/>

"""
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

>>> 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

>>> 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
##//////////////////////////////////////////////////////

[docs]class PositiveNaiveBayesClassifier(NaiveBayesClassifier):
[docs]    @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
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
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

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

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
##//////////////////////////////////////////////////////

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

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