Which of the following algorithms suffers from underflow (real numbers that are too small to be represented using double precision floats): rejection sampling, importance sampling, particle filtering? Explain why. How could underflow be avoided?

Exercise 9.16

(a) What are the independence assumptions made in the naive Bayes classifier for the help system of Example 9.36 (page 430).

(b) Are these independence assumptions reasonable? Explain why or why not.

(c) Suppose we have a topic-model network like the one of Figure 9.29 (page 435), but where all of the topics are parents of all of the words. What are all of the independencies of this model?

(d) Give an example where the topics would not be independent.