Probabilistic Graphical Models: Filling in the Information

Alexander Denev

In the previous chapter we showed how to build some simple PGMs that can encode our knowledge about how the real world “works” today in a visually appealing form. We hinted at the fact that both the structure and the parameters of a PGM can also be learnt from data. The final product of the reasoning and/or learning is a quantitative object called the joint probability distribution (JPD), which allows us to make inferences about the probability of occurrence of different configurations of variables in the problem. The task of deducing a JPD, in general, can be difficult. Luckily this is made simpler thanks to the master equation and the possibility of directional reasoning in the presence of posited causal links or evidence about spatial separation properties.

We have previously assumed that we already possess the information necessary to fill in the CPTs (or potentials) and our focus was on how to combine them to obtain a JPD. Things in real life are not that easy and we do not always have the necessary precise knowledge to pinpoint the building blocks of a PGM and their numerical attributes exactly. The world, in other words, is embedded with uncertainty, and, even if we use