Assume you are given the Bayes net and the corresponding CPTs shown in Figure S13.51. 

a. Assume we receive evidence that A = + a. If we were to draw samples using rejection sampling, what is the expected fraction of samples that will be rejected? 

b. Next, assume we observed both A = + a and D = + d. What are the weights for the following samples under likelihood weighting sampling?

(i) (+a, −b, +c, +d) 

(ii) (+a, −b, −c, +d) 

(iii) (+a, +b, −c, +d) 

c. Given the samples in the previous question, estimate P(−b | + a, +d). 

d. Assume we need to (approximately) answer two different inference queries for this graph: P(C | + a) and P(C | + d). You are required to answer one query using likelihood weighting and one query using Gibbs sampling. Which query would you answer with which algorithm? Justify your answer.

Figure S13.51

Transcribed Image Text:

B P(A) +a 0.1 -a 0.9 P(B) +b.7 -b.3 P(C|A, B) +c+a+b .25 -c+a+b.75 +c -a +b .6 -c -a +b 4 +c+a-b.5 -C +a -b .5 +c -a -b .2 -C-a -b 8 P(D|C) +d+c.5 -d +c.5 +d-c.8 -d-c.2