Mastering Probabilistic Graphical Models Using Python

Independencies in Markov networks

In the previous chapter, we saw how a Bayesian network structure encodes independency conditions in it, and how observing variables affects the flow of influence in the network. Similarly, in the case of Markov networks, the graph structure encodes independency conditions. However, the flow of influence in a Markov network stops as soon as any node is observed in that trail. This is quite different from what we saw in the Bayesian network, where different structures responded differently to the observation of the nodes.

To understand this more formally, let H be a Markov network structure and be a set of observed ...