We found that by changing the smoothing parameters of a Naive Bayes classifier, we could get far better accuracy numbers for certain tasks. By changing the Lidstone smoothing parameter from 0.05 to 0.5 or greater, we could go from an accuracy of about 50% to almost 70% on the task of question classification for question answering.

This is not at all surprising because, as described in an earlier post, the smoothing method used in the estimation of probabilities affects Naive Bayes classifiers greatly.

Below, we have provided an implementation of a Naive Bayes classifier which outperforms the Naive Bayes classifier supplied with NLTK 3.o by almost 10% on the task of classifying questions from the questions-train.txt file supplied with the textbook “Taming Text”.

Our Naive Bayes classifier (with a Lidstone smoothing parameter of 0.5) exhibits about 65% accuracy on the task of question classification, whereas the NLTK classifier has an accuracy of about 40% as shown below.

Finally, I’d like to say a few words about the import of this work.

Theoretically, by increasing the Lidstone smoothing parameter, we are merely compensating more strongly for absent features; we are negating the absence of a feature more vigorously; reducing the penalty for the absence of a feature in a specific category.

Because increased smoothing lowers the penalty for feature absence, it could help increase the accuracy when a data-set has many low-volume features that do not contribute to predicting a category, but whose chance presence and absence may be construed in the learning phase to be correlated with a category.

Further investigation is required before we can say whether the aforesaid hypothesis would explain **the effect of smoothing on the accuracy of classification** in regard to the question classification data-set that we used.

However, this exercise shows that algorithm implementations would do well to leave the choice of Lidstone smoothing parameters to the discretion of the end user of a Naive Bayes classifier.

The source code of our Naive Bayes classifier (using Lidstone smoothing) is provided below:

*This implementation of the Naive Bayes classifier was created by Geetanjali Rakshit, an intern at Aiaioo Labs.*

import numpy as np
import random
import sys, math
class Classifier:
def __init__(self, featureGenerator):
self.featureGenerator = featureGenerator
self._C_SIZE = 0
self._V_SIZE = 0
self._classes_list = []
self._classes_dict = {}
self._vocab = {}
def setClasses(self, trainingData):
for(label, line) in trainingData:
if label not in self._classes_dict.keys():
self._classes_dict[label] = len(self._classes_list)
self._classes_list.append(label)
self._C_SIZE = len(self._classes_list)
return
def getClasses(self):
return self._classes_list
def setVocab(self, trainingData):
index = 0;
for (label, line) in trainingData:
line = self.featureGenerator.getFeatures(line)
for item in line:
if(item not in self._vocab.keys()):
self._vocab[item] = index
index += 1
self._V_SIZE = len(self._vocab)
return
def getVocab(self):
return self._vocab
def train(self, trainingData):
pass
def classify(self, testData, params):
pass
def getFeatures(self, data):
return self.featureGenerator.getFeatures(data)
class FeatureGenerator:
def getFeatures(self, text):
text = text.lower()
return text.split()
class NaiveBayesClassifier(Classifier):
def __init__(self, fg, alpha = 0.05):
Classifier.__init__(self, fg)
self.__classParams = []
self.__params = [[]]
self.__alpha = alpha
def getParameters(self):
return (self.__classParams, self.__params)
def train(self, trainingData):
self.setClasses(trainingData)
self.setVocab(trainingData)
self.initParameters()
for (cat, document) in trainingData:
for feature in self.getFeatures(document):
self.countFeature(feature, self._classes_dict[cat])
def countFeature(self, feature, class_index):
counts = 1
self._counts_in_class[class_index][self._vocab[feature]] = self._counts_in_class[class_index][self._vocab[feature]] + counts
self._total_counts[class_index] = self._total_counts[class_index] + counts
self._norm = self._norm + counts
def classify(self, testData):
post_prob = self.getPosteriorProbabilities(testData)
return self._classes_list[self.getMaxIndex(post_prob)]
def getPosteriorProbabilities(self, testData):
post_prob = np.zeros(self._C_SIZE)
for i in range(0, self._C_SIZE):
for feature in self.getFeatures(testData):
post_prob[i] += self.getLogProbability(feature, i)
post_prob[i] += self.getClassLogProbability(i)
return post_prob
def getFeatures(self, testData):
return self.featureGenerator.getFeatures(testData)
def initParameters(self):
self._total_counts = np.zeros(self._C_SIZE)
self._counts_in_class = np.zeros((self._C_SIZE, self._V_SIZE))
self._norm = 0.0
def getLogProbability(self, feature, class_index):
return math.log(self.smooth(self.getCount(feature, class_index),self._total_counts[class_index]))
def getCount(self, feature, class_index):
if feature not in self._vocab.keys():
return 0
else:
return self._counts_in_class[class_index][self._vocab[feature]]
def smooth(self, numerator, denominator):
return (numerator + self.__alpha) / (denominator + (self.__alpha * len(self._vocab)))
def getClassLogProbability(self, class_index):
return math.log(self._total_counts[class_index]/self._norm)
def getMaxIndex(self, posteriorProbabilities):
maxi = 0
maxProb = posteriorProbabilities[maxi]
for i in range(0, self._C_SIZE):
if(posteriorProbabilities[i] >= maxProb):
maxProb = posteriorProbabilities[i]
maxi = i
return maxi
class Dataset:
def __init__(self, filename):
fp = open(filename, "r")
i = 0
self.__dataset = []
for line in fp:
if(line != "\n"):
line = line.split()
cat = line[0]
sent = ""
for word in range(1, len(line)):
sent = sent+line[word]+" "
sent = sent.strip()
self.__dataset.append([cat, str(sent)])
i = i+1
random.shuffle(self.__dataset)
self.__D_SIZE = i
self.__trainSIZE = int(0.6*self.__D_SIZE)
self.__testSIZE = int(0.3*self.__D_SIZE)
self.__devSIZE = 1 - (self.__trainSIZE + self.__testSIZE)
def setTrainSize(self, value):
self.__trainSIZE = int(value*0.01*self.__D_SIZE)
return self.__trainSIZE
def setTestSize(self, value):
self.__testSIZE = int(value*0.01*self.__D_SIZE)
return self.__testSIZE
def setDevelopmentSize(self):
self.__devSIZE = int(1 - (self.__trainSIZE + self.__testSIZE))
return self.__devSIZE
def getDataSize(self):
return self.__D_SIZE
def getTrainingData(self):
return self.__dataset[0:self.__trainSIZE]
def getTestData(self):
return self.__dataset[self.__trainSIZE:(self.__trainSIZE+self.__testSIZE)]
def getDevData(self):
return self.__dataset[0:self.__devSIZE]
#============================================================================================
if __name__ == "__main__":
# This Naive Bayes classifier implementation 10% better accuracy than the NLTK 3.0 Naive Bayes classifier implementation
# at the task of classifying questions in the question corpus distributed with the book "Taming Text".
# The "questions-train.txt" file can be found in the source code distributed with the book at https://www.manning.com/books/taming-text.
# To the best of our knowledge, the improvement in accuracy is owed to the smoothing methods described in our blog:
# https://aiaioo.wordpress.com/2016/01/29/in-a-naive-bayes-classifier-why-bother-with-smoothing-when-we-have-unknown-words-in-the-test-set/
filename = "questions-train.txt"
if len(sys.argv) > 1:
filename = sys.argv[1]
data = Dataset(filename)
data.setTrainSize(50)
data.setTestSize(50)
train_set = data.getTrainingData()
test_set = data.getTestData()
test_data = [test_set[i][1] for i in range(len(test_set))]
actual_labels = [test_set[i][0] for i in range(len(test_set))]
fg = FeatureGenerator()
alpha = 0.5 #smoothing parameter
nbClassifier = NaiveBayesClassifier(fg, alpha)
nbClassifier.train(train_set)
correct = 0;
total = 0;
for line in test_data:
best_label = nbClassifier.classify(line)
if best_label == actual_labels[total]:
correct += 1
total += 1
acc = 1.0*correct/total
print("Accuracy of this Naive Bayes Classifier: "+str(acc))

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