Shape Color Label Circle Blue 1 Circle Blue 0 Circle Green 0 Diamond Blue 0 Diamond...

 

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Shape Color Label Circle Blue 1 Circle Blue 0 Circle Green 0 Diamond Blue 0 Diamond Green 0 Diamond Green 0 Diamond Red 1 Square Blue 1 Square Square Red 1 Red 1 (a) What are the parameters of the Nave Bayes model estimated using maximum likelihood estima- tion? (b) What is a testing example (Shape, Color) for which the maximum likelihood Nave Bayes model provides an undefined posterior label probability (i.e., 0/0)? (c) What are the parameters of the Nave 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 Nave Bayes model? (e) Explain in your own words why Laplace Smoothing is important for Naive Bayes models. Shape Color Label Circle Blue 1 Circle Blue 0 Circle Green 0 Diamond Blue 0 Diamond Green 0 Diamond Green 0 Diamond Red 1 Square Blue 1 Square Square Red 1 Red 1 (a) What are the parameters of the Nave Bayes model estimated using maximum likelihood estima- tion? (b) What is a testing example (Shape, Color) for which the maximum likelihood Nave Bayes model provides an undefined posterior label probability (i.e., 0/0)? (c) What are the parameters of the Nave 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 Nave Bayes model? (e) Explain in your own words why Laplace Smoothing is important for Naive Bayes models.