# Chapter 5. Approximate Inference

This chapter introduces a second class of inference algorithms, maybe the most important of all because of their versatility. The approach is completely different from what we have seen until now. Indeed, we saw two classes of algorithms, one based on a pure analytic resolution of the problem by calculating manually the posterior distribution and the other one by using message propagation in a graph. In both cases, the result was computed exactly. In the case of an analytic solution, computing the solution usually boils down to computing a function of the posterior distribution. In the case of a message-passing algorithm, computing the posterior distribution is done step-by-step by propagating messages on a graph. If the graph is not appropriate for this type of algorithm, the computations can be extremely long and often intractable.

However, in many cases, we can trade a bit of accuracy for more speed. This is the main idea of approximate inference...