# Question: This exercise is concerned with the variable elimination algorithm in

This exercise is concerned with the variable elimination algorithm in Figure.

a. Section 14.4 applies variable elimination t the query P (Burglary│JohnCalls = true, Mary Calls = true). Perform the calculations indicated and check the answer is correct.

b. Count the number of arithmetic operations performed, and compares it with the number performed by the enumeration algorithm.

c. Suppose a network has the form of a chain: a sequence of Boolean variables X1... Xn where Parents (Xi) = {X i_1} for i = 2... n. What is the complexity of computing P (X1│Xn = true) using enumeration? Using variable elimination?

d. Prove that the complexity of running variable elimination on a poly-tree network is linear in the size of the tree for any variable ordering consistent with the network structure.

a. Section 14.4 applies variable elimination t the query P (Burglary│JohnCalls = true, Mary Calls = true). Perform the calculations indicated and check the answer is correct.

b. Count the number of arithmetic operations performed, and compares it with the number performed by the enumeration algorithm.

c. Suppose a network has the form of a chain: a sequence of Boolean variables X1... Xn where Parents (Xi) = {X i_1} for i = 2... n. What is the complexity of computing P (X1│Xn = true) using enumeration? Using variable elimination?

d. Prove that the complexity of running variable elimination on a poly-tree network is linear in the size of the tree for any variable ordering consistent with the network structure.

**View Solution:**## Answer to relevant Questions

Investigate the complexity of exact inference in general Bayesian networks:a. Prove that any 3-SAT problem can be reduced to exact inference in a Bayesian network constructed to represent the particular problem and hence ...Show that any second-order Markov process can be rewritten as a first-order Markov process with an augmented set of state variables. Can this always he done parsimoniously that is, without increasing the number of parameters ...Show how to represent an HMM as a recursive relational probabilistic model, as suggested in Section 14.6.Write a computer program to automate the process in Exercise 16.4. Try your program out on several people of different net worth and political outlook. Comment on the consistency of your results, both for an individual and ...Suppose that we define the utility of a state sequence to be the maximum reward obtained in any state in the sequence. Show that this utility function does not result in stationary preferences between state sequences. Is it ...Post your question