/
naivebayes.py
236 lines (197 loc) · 9.46 KB
/
naivebayes.py
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
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
# Natural Language Toolkit: Naive Bayes Classifiers
#
# Copyright (C) 2001-2012 NLTK Project
# Author: Edward Loper <edloper@gradient.cis.upenn.edu>
# URL: <http://www.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(featues) explicitly, the algorithm just
calculates the denominator 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 collections import defaultdict
from nltk.probability import FreqDist, DictionaryProbDist, ELEProbDist, sum_logs
from 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 = 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 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, str(l1)[:6], str(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) ]
"""
# 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.
features = sorted(features,
key=lambda feature: minprob[feature]/maxprob[feature])
return features[:n]
@staticmethod
def train(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.inc(label)
for fname, fval in featureset.items():
# Increment freq(fval|label, fname)
feature_freqdist[label, fname].inc(fval)
# 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()
feature_freqdist[label, fname].inc(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 NaiveBayesClassifier(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()