Mastering Probabilistic Graphical Models Using Python

Relating graphs and distributions

In the restaurant example or the late-for-school example, we used the Bayesian network to represent the independencies in the random variables. We also saw that we can use the Bayesian network to represent the joint probability distribution over all the variables using the chain rule. In this section, we will unify these two concepts and show that a probability distribution D can only be represented using a graph G, if and only if D can be represented as a set of CPDs associated with the graph G.

IMAP

A graph object G is called an IMAP of a probability distribution D if the set of independency assertions in G, denoted by I(G), is a subset of the set of independencies in D, denoted by I(D).

Let's take an example of ...