Sampling from a distribution

We have a big problem with probabilistic graphical models in general: they are intractable. They quickly become so complex that it is impossible to run anything in a reasonable amount of time. Not to mention learning them. Remember, for a simple algorithm such as EM, we need to compute a posterior distribution at each iteration. If the dataset is big, which is common now, if the model has a lot of dimensions, which is also common, it becomes totally prohibitive. Moreover, we limited ourselves to a small class of distributions, such as multinomial or Gaussian distributions. Even if they can cover a wide range of applications, it's not the case all the time.

In this chapter, we consider a new class of algorithms based on the idea of sampling from a distribution. Sampling here means to draw values of the parameters at random, following a particular distribution. For example, if one throws a dice, one draws a sample from a multinomial distribution, such that six values...