smile.classification

Class NaiveBayes

java.lang.Object

smile.classification.NaiveBayes

All Implemented Interfaces:

java.io.Serializable, Classifier<double[]>, OnlineClassifier<double[]>, SoftClassifier<double[]>

public class NaiveBayes
extends java.lang.Object
implements OnlineClassifier<double[]>, SoftClassifier<double[]>, java.io.Serializable

Naive Bayes classifier. A naive Bayes classifier is a simple probabilistic classifier based on applying Bayes' theorem with strong (naive) independence assumptions. Depending on the precise nature of the probability model, naive Bayes classifiers can be trained very efficiently in a supervised learning setting.

In spite of their naive design and apparently over-simplified assumptions, naive Bayes classifiers have worked quite well in many complex real-world situations and are very popular in Natural Language Processing (NLP).

For a general purpose naive Bayes classifier without any assumptions about the underlying distribution of each variable, we don't provide a learning method to infer the variable distributions from the training data. Instead, the users can fit any appropriate distributions on the data by themselves with various Distribution classes. Although the predict(double[]) method takes an array of double values as a general form of independent variables, the users are free to use any discrete distributions to model categorical or ordinal random variables.

For document classification in NLP, there are two different ways we can set up an naive Bayes classifier: multinomial model and Bernoulli model. The multinomial model generates one term from the vocabulary in each position of the document. The multivariate Bernoulli model or Bernoulli model generates an indicator for each term of the vocabulary, either indicating presence of the term in the document or indicating absence. Of the two models, the Bernoulli model is particularly sensitive to noise features. A Bernoulli naive Bayes classifier requires some form of feature selection or else its accuracy will be low.

The different generation models imply different estimation strategies and different classification rules. The Bernoulli model estimates as the fraction of documents of class that contain term. In contrast, the multinomial model estimates as the fraction of tokens or fraction of positions in documents of class that contain term. When classifying a test document, the Bernoulli model uses binary occurrence information, ignoring the number of occurrences, whereas the multinomial model keeps track of multiple occurrences. As a result, the Bernoulli model typically makes many mistakes when classifying long documents. However, it was reported that the Bernoulli model works better in sentiment analysis.

The models also differ in how non-occurring terms are used in classification. They do not affect the classification decision in the multinomial model; but in the Bernoulli model the probability of nonoccurrence is factored in when computing. This is because only the Bernoulli model models absence of terms explicitly.

See Also:

Distribution, LDA, QDA,

References

1. Christopher D. Manning, Prabhakar Raghavan, and Hinrich Schutze. Introduction to Information Retrieval, Chapter 13, 2009.

, Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	NaiveBayes.Model The generation models of naive Bayes classifier.
static class	NaiveBayes.Trainer Trainer for naive Bayes classifier for document classification.

Constructor Summary

Constructors

Constructor and Description
NaiveBayes(double[] priori, Distribution[][] condprob) Constructor of general naive Bayes classifier.
NaiveBayes(NaiveBayes.Model model, double[] priori, int p) Constructor of naive Bayes classifier for document classification.
NaiveBayes(NaiveBayes.Model model, double[] priori, int p, double sigma) Constructor of naive Bayes classifier for document classification.
NaiveBayes(NaiveBayes.Model model, int k, int p) Constructor of naive Bayes classifier for document classification.
NaiveBayes(NaiveBayes.Model model, int k, int p, double sigma) Constructor of naive Bayes classifier for document classification.

Method Summary

Modifier and Type	Method and Description
double[]	getPriori() Returns a priori probabilities.
void	learn(double[][] x, int[] y) Online learning of naive Bayes classifier on sequences, which are modeled as a bag of words.
void	learn(double[] x, int y) Online learning of naive Bayes classifier on a sequence, which is modeled as a bag of words.
void	learn(SparseArray x, int y) Online learning of naive Bayes classifier on a sequence, which is modeled as a bag of words.
int	predict(double[] x) Predict the class of an instance.
int	predict(double[] x, double[] posteriori) Predict the class of an instance.
int	predict(SparseArray x) Predict the class of an instance.
int	predict(SparseArray x, double[] posteriori) Predict the class of an instance.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface smile.classification.Classifier

predict

Constructor Detail

NaiveBayes

public NaiveBayes(double[] priori,
                  Distribution[][] condprob)

Constructor of general naive Bayes classifier.

Parameters:

priori - the priori probability of each class.

condprob - the conditional distribution of each variable in each class. In particular, condprob[i][j] is the conditional distribution P(x_j | class i).

NaiveBayes

public NaiveBayes(NaiveBayes.Model model,
                  int k,
                  int p)

Constructor of naive Bayes classifier for document classification. The priori probability of each class will be learned from data. By default, we use add-one/Laplace smoothing, which simply adds one to each count to eliminate zeros. Add-one smoothing can be interpreted as a uniform prior (each term occurs once for each class) that is then updated as evidence from the training data comes in.

Parameters:

model - the generation model of naive Bayes classifier.

k - the number of classes.

p - the dimensionality of input space.

NaiveBayes

public NaiveBayes(NaiveBayes.Model model,
                  int k,
                  int p,
                  double sigma)

Constructor of naive Bayes classifier for document classification. The priori probability of each class will be learned from data. Add-k smoothing.

Parameters:

model - the generation model of naive Bayes classifier.

k - the number of classes.

p - the dimensionality of input space.

sigma - the prior count of add-k smoothing of evidence.

NaiveBayes

public NaiveBayes(NaiveBayes.Model model,
                  double[] priori,
                  int p)

Constructor of naive Bayes classifier for document classification. By default, we use add-one/Laplace smoothing, which simply adds one to each count to eliminate zeros. Add-one smoothing can be interpreted as a uniform prior (each term occurs once for each class) that is then updated as evidence from the training data comes in.

Parameters:

model - the generation model of naive Bayes classifier.

priori - the priori probability of each class.

p - the dimensionality of input space.

NaiveBayes

public NaiveBayes(NaiveBayes.Model model,
                  double[] priori,
                  int p,
                  double sigma)

Constructor of naive Bayes classifier for document classification. Add-k smoothing.

Parameters:

model - the generation model of naive Bayes classifier.

priori - the priori probability of each class.

p - the dimensionality of input space.

sigma - the prior count of add-k smoothing of evidence.

Method Detail

getPriori

public double[] getPriori()

Returns a priori probabilities.

learn

public void learn(double[] x,
                  int y)

Online learning of naive Bayes classifier on a sequence, which is modeled as a bag of words. Note that this method is NOT applicable for naive Bayes classifier with general generation model.

Specified by:

learn in interface OnlineClassifier<double[]>

Parameters:

x - training instance.

y - training label in [0, k), where k is the number of classes.

learn

public void learn(SparseArray x,
                  int y)

Online learning of naive Bayes classifier on a sequence, which is modeled as a bag of words. Note that this method is NOT applicable for naive Bayes classifier with general generation model.

Parameters:

x - training instance in sparse format.

y - training label in [0, k), where k is the number of classes.

learn

public void learn(double[][] x,
                  int[] y)

Online learning of naive Bayes classifier on sequences, which are modeled as a bag of words. Note that this method is NOT applicable for naive Bayes classifier with general generation model.

Parameters:

x - training instances.

y - training labels in [0, k), where k is the number of classes.

predict

public int predict(double[] x)

Predict the class of an instance.

Specified by:

predict in interface Classifier<double[]>

Parameters:

x - the instance to be classified.

Returns:

the predicted class label. For MULTINOMIAL and BERNOULLI models, returns -1 if the instance does not contain any feature words.

predict

public int predict(double[] x,
                   double[] posteriori)

Predict the class of an instance.

Specified by:

predict in interface SoftClassifier<double[]>

Parameters:

x - the instance to be classified.

posteriori - the array to store a posteriori probabilities on output.

Returns:

the predicted class label. For MULTINOMIAL and BERNOULLI models, returns -1 if the instance does not contain any feature words.

predict

public int predict(SparseArray x)

Predict the class of an instance.

Parameters:

x - the instance to be classified.

Returns:

the predicted class label. For MULTINOMIAL and BERNOULLI models, returns -1 if the instance does not contain any feature words.

predict

public int predict(SparseArray x,
                   double[] posteriori)

Predict the class of an instance.

Parameters:

x - the instance to be classified.

posteriori - the array to store a posteriori probabilities on output.

Returns:

the predicted class label. For MULTINOMIAL and BERNOULLI models, returns -1 if the instance does not contain any feature words.