# Natural Language Toolkit: Naive Bayes Classifiers # # Copyright (C) 2001-2010 NLTK Project # Author: Edward Loper # URL: # For license information, see LICENSE.TXT # # $Id: naivebayes.py 2063 2004-07-17 21:02:24Z edloper $ """ 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 nltk.compat import defaultdict from nltk.probability import * from api import * ##////////////////////////////////////////////////////// ## 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 L{ProbDistI} whose samples are labels. I.e., P(label) = C{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 C{(label,fname)} pairs and whose values are L{ProbDistI}s over feature values. I.e., P(fname=fval|label) = C{feature_probdist[label,fname].prob(fval)}. If a given C{(label,fname)} is not a key in C{feature_probdist}, then it is assumed that the corresponding P(fname=fval|label) is 0 for all values of C{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, l1[:6], 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 C{(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 C{(featureset, label)}. """ label_freqdist = FreqDist() feature_freqdist = defaultdict(FreqDist) feature_values = defaultdict(set) fnames = set() # Count up how many times each feature value occured, 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()