Learning Probabilistic Graphical Models in R

Sum-product and belief updates

When computing the distribution of one variable (or a subset of variables), the main operation is the marginalization, which consists of summing over a variable (or a subset of variables) to eliminate it from the main expression. If we call ϕ a factor in the factorization of the joint distribution, we can use the following properties to generalize and improve the variable elimination algorithm we saw in the previous section:

• Commutativity:
• Associativity:
• And if

If again we apply it to the joint distribution P(ABCD)