Learning with hidden variables – the EM algorithm
The last part of this chapter is an important algorithm that we will use again in the course of this book. It is a very general algorithm used to learn probabilistic models in which variables are hidden; that is, some of the variables are not observed. Models with hidden variables are sometimes called latent variable models. The EM algorithm is a solution to this kind of problem and goes very well with probabilistic graphical models.
Most of the time, when we want to learn the parameters of a model, we write an objective function, such as the likelihood function, and we aim at finding the parameters that maximize this function. Generally speaking, one could simply use a black-box numerical optimizer and just compute the relevant parameters given this function. However, in many cases, this would be intractable and too prone to numerical errors (due to the inherent approximations done by CPUs). Therefore it is generally not a good solution...
