Problem 4 The on-line material for this text provides a version of both the Logic Sampling algorithm (Algorithm 3.3) and the LikelihoodWeighting algorithm (Algorithm 3.4).

Take an example BN (either provided with the online material, or that you’ve developed for the problems set in Chapter 2) and do the following.

1. Run the BN software to obtain the exact inference result.

2. Run the LS Algorithm, printing out the approximate beliefs every 10 iterations and stopping when a certain level of convergence has been achieved.

3. Do the same for the LW algorithm.

4. As we have seen, the Kullback-Leibler divergence (????3.6.5) can be used to measure the error in the beliefs obtained using an approximate inference algorithm.

Compute and plot the KL error over time for both the LS and LW algorithm.

5. Investigate what effect the following changes may have on the error for the LW algorithm.

???? Vary the priors between (i) more uniform and (ii) more extreme.

???? Vary the location of the evidence (i) root, (ii) intermediate and (iii) leaf.

???? Set evidence that is more or less likely.