Statistical Details for the Naive Bayes Platform

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Predictive and Specialized Modeling • Naive Bayes • Statistical Details for the Naive Bayes Platform

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Algorithm

The naive Bayes method classifies an observation into the class for which its probability of membership, given the values of its features, is highest. The method assumes that the features are conditionally independent within each class.

Denote the possible classifications by C1, …, Ck. Denote the features, or predictors, by X1, X2, …, Xp.

The conditional probability that an observation with Xj = xj belongs to the class Cr is given as follows:

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If Xj is categorical: P(Cr|xj)

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If Xj is continuous:

Here, φ is the standard normal density function, and m and s are the mean and standard deviation, respectively, of the predictor values within the class Cr.

The conditional probability of that an observation with predictor values x1, x2, …, xp belongs in the class Cr is computed as follows:

An observation is classified into the class for which its conditional probability is the largest.

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Help created on 9/19/2017