Book Image

Mastering Probabilistic Graphical Models with Python

By : Ankur Ankan
Book Image

Mastering Probabilistic Graphical Models with Python

By: Ankur Ankan

Overview of this book

Table of Contents (14 chapters)
Mastering Probabilistic Graphical Models Using Python
Credits
About the Authors
About the Reviewers
www.PacktPub.com
Preface
Index

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 variables. Then, the path is active if and only if none of the for are in Z.

In the case of Bayesian networks, we had the concept of local independencies, where a variable is independent of all its non-descendants, given given its parents. We also had global conditions which were implied by D-Separation. Similarly, in the case of Markov networks...