# Natural Language Toolkit: Naive Bayes Classifiers
#
# Copyright (C) 2001-2019 NLTK Project
# Author: Edward Loper <edloper@gmail.com>
# URL: <http://nltk.org/>
# For license information, see LICENSE.TXT
"""
A classifier based on the Naive Bayes algorithm. In order to find the
probability for a label, this algorithm first uses the Bayes rule to
express P(label|features) in terms of P(label) and P(features|label):
| P(label) * P(features|label)
| P(label|features) = ------------------------------
| P(features)
The algorithm then makes the 'naive' assumption that all features are
independent, given the label:
| P(label) * P(f1|label) * ... * P(fn|label)
| P(label|features) = --------------------------------------------
| P(features)
Rather than computing P(features) explicitly, the algorithm just
calculates the numerator for each label, and normalizes them so they
sum to one:
| P(label) * P(f1|label) * ... * P(fn|label)
| P(label|features) = --------------------------------------------
| SUM[l]( P(l) * P(f1|l) * ... * P(fn|l) )
"""
from __future__ import print_function, unicode_literals
from collections import defaultdict
from nltk.probability import FreqDist, DictionaryProbDist, ELEProbDist, sum_logs
from nltk.classify.api import ClassifierI
##//////////////////////////////////////////////////////
## Naive Bayes Classifier
##//////////////////////////////////////////////////////
class NaiveBayesClassifier(ClassifierI):
"""
A Naive Bayes classifier. Naive Bayes classifiers are
paramaterized by two probability distributions:
- P(label) gives the probability that an input will receive each
label, given no information about the input's features.
- P(fname=fval|label) gives the probability that a given feature
(fname) will receive a given value (fval), given that the
label (label).
If the classifier encounters an input with a feature that has
never been seen with any label, then rather than assigning a
probability of 0 to all labels, it will ignore that feature.
The feature value 'None' is reserved for unseen feature values;
you generally should not use 'None' as a feature value for one of
your own features.
"""
def __init__(self, label_probdist, feature_probdist):
"""
:param label_probdist: P(label), the probability distribution
over labels. It is expressed as a ``ProbDistI`` whose
samples are labels. I.e., P(label) =
``label_probdist.prob(label)``.
:param feature_probdist: P(fname=fval|label), the probability
distribution for feature values, given labels. It is
expressed as a dictionary whose keys are ``(label, fname)``
pairs and whose values are ``ProbDistI`` objects over feature
values. I.e., P(fname=fval|label) =
``feature_probdist[label,fname].prob(fval)``. If a given
``(label,fname)`` is not a key in ``feature_probdist``, then
it is assumed that the corresponding P(fname=fval|label)
is 0 for all values of ``fval``.
"""
self._label_probdist = label_probdist
self._feature_probdist = feature_probdist
self._labels = list(label_probdist.samples())
def labels(self):
return self._labels
def classify(self, featureset):
return self.prob_classify(featureset).max()
def prob_classify(self, featureset):
# Discard any feature names that we've never seen before.
# Otherwise, we'll just assign a probability of 0 to
# everything.
featureset = featureset.copy()
for fname in list(featureset.keys()):
for label in self._labels:
if (label, fname) in self._feature_probdist:
break
else:
# print 'Ignoring unseen feature %s' % fname
del featureset[fname]
# Find the log probabilty of each label, given the features.
# Start with the log probability of the label itself.
logprob = {}
for label in self._labels:
logprob[label] = self._label_probdist.logprob(label)
# Then add in the log probability of features given labels.
for label in self._labels:
for (fname, fval) in featureset.items():
if (label, fname) in self._feature_probdist:
feature_probs = self._feature_probdist[label, fname]
logprob[label] += feature_probs.logprob(fval)
else:
# nb: This case will never come up if the
# classifier was created by
# NaiveBayesClassifier.train().
logprob[label] += sum_logs([]) # = -INF.
return DictionaryProbDist(logprob, normalize=True, log=True)
def show_most_informative_features(self, n=10):
# Determine the most relevant features, and display them.
cpdist = self._feature_probdist
print('Most Informative Features')
for (fname, fval) in self.most_informative_features(n):
def labelprob(l):
return cpdist[l, fname].prob(fval)
labels = sorted(
[l for l in self._labels if fval in cpdist[l, fname].samples()],
key=labelprob,
)
if len(labels) == 1:
continue
l0 = labels[0]
l1 = labels[-1]
if cpdist[l0, fname].prob(fval) == 0:
ratio = 'INF'
else:
ratio = '%8.1f' % (
cpdist[l1, fname].prob(fval) / cpdist[l0, fname].prob(fval)
)
print(
(
'%24s = %-14r %6s : %-6s = %s : 1.0'
% (fname, fval, ("%s" % l1)[:6], ("%s" % l0)[:6], ratio)
)
)
def most_informative_features(self, n=100):
"""
Return a list of the 'most informative' features used by this
classifier. For the purpose of this function, the
informativeness of a feature ``(fname,fval)`` is equal to the
highest value of P(fname=fval|label), for any label, divided by
the lowest value of P(fname=fval|label), for any label:
| max[ P(fname=fval|label1) / P(fname=fval|label2) ]
"""
if hasattr(self, '_most_informative_features'):
return self._most_informative_features[:n]
else:
# The set of (fname, fval) pairs used by this classifier.
features = set()
# The max & min probability associated w/ each (fname, fval)
# pair. Maps (fname,fval) -> float.
maxprob = defaultdict(lambda: 0.0)
minprob = defaultdict(lambda: 1.0)
for (label, fname), probdist in self._feature_probdist.items():
for fval in probdist.samples():
feature = (fname, fval)
features.add(feature)
p = probdist.prob(fval)
maxprob[feature] = max(p, maxprob[feature])
minprob[feature] = min(p, minprob[feature])
if minprob[feature] == 0:
features.discard(feature)
# Convert features to a list, & sort it by how informative
# features are.
self._most_informative_features = sorted(
features, key=lambda feature_: minprob[feature_] / maxprob[feature_]
)
return self._most_informative_features[:n]
@classmethod
def train(cls, labeled_featuresets, estimator=ELEProbDist):
"""
:param labeled_featuresets: A list of classified featuresets,
i.e., a list of tuples ``(featureset, label)``.
"""
label_freqdist = FreqDist()
feature_freqdist = defaultdict(FreqDist)
feature_values = defaultdict(set)
fnames = set()
# Count up how many times each feature value occurred, given
# the label and featurename.
for featureset, label in labeled_featuresets:
label_freqdist[label] += 1
for fname, fval in featureset.items():
# Increment freq(fval|label, fname)
feature_freqdist[label, fname][fval] += 1
# Record that fname can take the value fval.
feature_values[fname].add(fval)
# Keep a list of all feature names.
fnames.add(fname)
# If a feature didn't have a value given for an instance, then
# we assume that it gets the implicit value 'None.' This loop
# counts up the number of 'missing' feature values for each
# (label,fname) pair, and increments the count of the fval
# 'None' by that amount.
for label in label_freqdist:
num_samples = label_freqdist[label]
for fname in fnames:
count = feature_freqdist[label, fname].N()
# Only add a None key when necessary, i.e. if there are
# any samples with feature 'fname' missing.
if num_samples - count > 0:
feature_freqdist[label, fname][None] += num_samples - count
feature_values[fname].add(None)
# Create the P(label) distribution
label_probdist = estimator(label_freqdist)
# Create the P(fval|label, fname) distribution
feature_probdist = {}
for ((label, fname), freqdist) in feature_freqdist.items():
probdist = estimator(freqdist, bins=len(feature_values[fname]))
feature_probdist[label, fname] = probdist
return cls(label_probdist, feature_probdist)
##//////////////////////////////////////////////////////
## Demo
##//////////////////////////////////////////////////////
def demo():
from nltk.classify.util import names_demo
classifier = names_demo(NaiveBayesClassifier.train)
classifier.show_most_informative_features()
if __name__ == '__main__':
demo()
