In this chapter, we discussed two algorithms, namely variable elimination and belief propagation, to find the conditional probability and do MAP queries on the models. We also discussed how the elimination order of variables in variable elimination affects the running complexity of the algorithm. To select efficient ordering, we discussed a few algorithms. Then, we discussed MAP queries, using which we can approach our machine learning problems through graphical models. We also compared variable elimination and belief propagation and discussed the benefits of each of these and when to use them.

In the next chapter, we will discuss various algorithms for approximate inference, including sampling methods, using which we can do approximate inference over models. Approximate methods help us save computation when we don't need the computations to be exact.