Marginalization and Conditioning for LWF Chain Graphs
This work addresses theoretical challenges in graphical models for probabilistic inference, but it appears incremental as it builds on existing LWF chain graph frameworks.
The paper tackles the problem of marginalization and conditioning on subsets of nodes in chain graphs with the LWF Markov property by defining chain mixed graphs (CMGs) and anterial graphs, providing separation criteria and methods for generating these graphs after such operations.
In this paper, we deal with the problem of marginalization over and conditioning on two disjoint subsets of the node set of chain graphs (CGs) with the LWF Markov property. For this purpose, we define the class of chain mixed graphs (CMGs) with three types of edges and, for this class, provide a separation criterion under which the class of CMGs is stable under marginalization and conditioning and contains the class of LWF CGs as its subclass. We provide a method for generating such graphs after marginalization and conditioning for a given CMG or a given LWF CG. We then define and study the class of anterial graphs, which is also stable under marginalization and conditioning and contains LWF CGs, but has a simpler structure than CMGs.