1. Naïve Bayes Consider the following dataset: Shape Circle Color Label Blue 1 Circle Blue Green Circle Diamond Blue Green Green Diamond Diamond Diamond Red 1 Square Square Square Blue 1 Red 1 Red 1 (a) What are the parameters of the Naïve Bayes model estimated using maximum likelihood estima- tion? (b) What is a testing example (Shape, Color) for which the maximum likelihood Naïve Bayes model provides an undefined posterior label probability (i.e., 0/0)? (c) What are the parameters of the Naïve Bayes model using Laplacian smoothing with a pseudo- count of 1? (d) What is the posterior label probability for your example from part (b) under the Laplacian- smoothed Naiïve Bayes model?

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