M. Studeny: A recovery algorithm for chain graphs. International Journal of Approximate Reasoning 17 (1997), n. 2-3, pp. 265-293.

The class of chain graphs involving both undirected graphs and directed acyclic graphs was introduced in middle eighties for description of probabilistic conditional independence structures. Every class of Markov equivalent chain graphs (that is, the graphs describing the same conditional independence structure) has a natural representative, which is called the largest chain graph. The paper presents a recovery algorithm, which on the basis of the conditional independence structure induced by a chain graph finds the largest chain graph, representing the corresponding class of Markov equivalent chain graphs. As a byproduct an undirect (implicit) graphical characterization of the graphs, which are the largest chain graphs (for a class of Markov equivalent chain graphs) is obtained, and an algorithm changing every chain graph into the largest chain graph of the corresponding equivalence class is described.

AMS classification 68T30, 62H05

chain graph
Markov equivalence
largest chain graph
pool-component principle

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The paper builds on the following works: