Naive Bayes

The Naive Bayes is an algorithm for classification. Let’s first define Naive Bayes it for two categories. \(Y\) is either in category \(A\) or category \(B\) where \(Y\) has features notated as the random variable \(\Phi=\set{\phi_1,\phi_2,\ldots,\phi_n}\)

\[ O = \frac{P(A|\Phi)}{P(B|\Phi)} = \frac{\prod{P(A|\phi_i)}}{\prod{P(B|\phi_i)}} \]

• This formula is interpreted as the odds that \(Y\) is either \(A\) vs \(B\) given \(\Phi\)

• Naive Bayes is naive simply because we assume a commutative/independent relation between each feature (order does not matter).

Python - sklearn

Naive bayes package: sklearn.naive_bayes

from sklearn.naive_bayes import __NB
clf = __NB()
clf.fit(X_train, Y_train)
Y_pred = clf.predict(X_test)