Extensions of HMM

In the previous sections, we discussed HMM, sampling from it and evaluating the probability of a given sequence given its parameters. In this section, we are going to discuss some of its variations.

Factorial HMMs

Let's consider the problem of modelling of several objects in a sequence of images. If there are M objects with K different positions and orientations in the image, there are be K^M possible states for the system underlying an image. An HMM would require K^M distinct states to model the system. This way of representing the system is not only inefficient but also difficult to interpret. We would prefer that our HMM could capture the state space by using M different K-dimensional variables.

A factorial...