Bayesian Networks (BNs) are popular graphical models for the representation of statistical problems embodying dependence relationships between a number of variables. Much of this popularity is due to the d-separation theorem of Pearl and Lauritzen, which allows an analyst to identify the conditional independence statements that a model of the problem embodies using only the topology of the grap...

Graphs provide an excellent framework for interrogating symmetric models of measurement random variables and discovering their implied conditional independence structure. However, it is not unusual for a model to be specified from a description of how a process unfolds (i.e. via its event tree), rather than through relationships between a given set of measurements. Here we introduce a new mixed...

%'c shw that perfectly orderabk grapk Sa are q&-parity graphs by exhibiting two &lodes which are not llinked by a chordless odd chain. This proof is short and simpler than the one given by H. Meynid. A graph G = (V, E) _ is called a quasi-~&y graph if for every A s X the induced subgraph GA is a clique or contains 2 nodes x, y which are riot linked by a (chordless) odd chain in G,+ Quasi-parity...

A chain probe graph is a graph that admits an independent set S of vertices and a set F of pairs of elements of S such that G+ F is a chain graph (i.e., a 2K2-free bipartite graph). We show that chain probe graphs are exactly the bipartite graphs that do not contain as an induced subgraph a member of a family of six forbidden subgraphs, and deduce an O(n2) recognition algorithm. Given a class C...

This paper proposes a new approach for designing learning bayesian network algorithms that explore the structure equivalence classes space. Its main originality consists in the representation of equivalence classes by largest chain graphs, instead of essential graphs which are generally used in the similar task. We show that this approach drastically simplifies the algorithms formulation and ha...