1.       Na¨ıve Bayes is a generative model in which each class corresponds to one mixture component. Design a semi-supervised generalization of the nai¨ıve Bayes model in which each of the k classes contains exactly b > 1 mixture components for a total of b · k mixture components. How would you perform parameter estimation in this model?

2.       The adaptive nearest-neighbor method discussed in the chapter uses a single distortion metric over the entire data space in order to compute the nearest neighbor of a point. Propose a training algorithm to make this metric locally adaptive, so that an optimized distortion metric is used for each test instance based on the local class patterns in the data. What are the possible advantages and disadvantages of using such an approach?