LO 7.2.2.C

Learning Objective: Explain why Naïve Bayes calculations are done in log space so that the predicted class is a linear function of input features.

Review:

• Naïve Bayes calculations.

The returned class  is the class associated with the maximum posterior probability given a set of features f1, f2,...,fn. The max posterior probability can be formulated as a product chain

The issue with this formulation is that a product chain is not computational “friendly”. Therefore, to avoid underflow and increase speed, we usually “linearize” the max posterior probability by transforming it in log space as follows: