Variable Elimination Algorithm - Engineering Assignment Help

Assignment Task

Consider the following belief network with binary random variables.

(Source: Adapted from Poole and Mackworth, Artificial Intelligence 2E, Section 8.3.2. For a description of the meaning of the variables in this belief network, see Example 8.15.) Suppose we want to compute a probability distribution over T given the evidence S = 1 and R = 1. That is, we want to compute P(T = 0|S = 1, R = 1) and P(T = 1|S = 1, R = 1). In this question, we will evaluate the efficiency of two different methods of computing these probabilities. The conditional probabilities of this belief network (expressed as factor tables) are as follows:

Note that the conditional probabilities are specified with some redundancy. For example, the tables store both P(A = 0|T = 1, F = 1) and P(A = 1|T = 1, F = 1), even though this information is technically redundant. Therefore, no addition or subtraction operations are required to compute P(A = 0|T = 1, F = 1) based on P(A = 1|T = 1, F = 1) or vice versa.

(a) Computation using variable elimination Use the variable elimination algorithm (with elimination order S, R, L, A, F) to compute P(T = 0|S = 1, R = 1) and P(T = 1|S = 1, R = 1). You do not need to write code for this; you should apply the algorithm step-by-step and show your work, including any new factor tables that are computed along the way.

(b) Counting calculations used by the variable elimination algorithm In the following table, fill in the number of multiplication, addition, and division operations needed for each phase of the VE algorithm. You should count operations using the same method used in class: for example, a × b + c × d + e × f involves 3 multiplications and 2 additions.

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