Iterative Proportional Fitting (IPF), com­ bined with EM, is commonly used as an al­ gorithm for likelihood maximization in undi­ rected graphical models. In this paper, we present two iterative algorithms that gener­ alize upon IPF. The first one is for likelihood maximization in discrete chain factor graphs, which we define as a wide class of discrete variable models including undirected grap...

For a given graph G, maximum internal spanning tree of G is with number vertices. The Maximum Internal Spanning Tree (MIST) problem to find the graph. MIST generalization Hamiltonian path problem. Since NP-hard, even for bipartite and chordal graphs, two important subclasses also remains NP-hard these classes. In this paper, we propose linear-time algorithms compute cographs, block cactus chain...

This paper deals with chain graphs under the classic Lauritzen-Wermuth-Frydenberg interpretation. We prove that the strictly positive discrete probability distributions with the prescribed sample space that factorize according to a chain graph G with dimension d have positive Lebesgue measure wrt R, whereas those that factorize according to G but are not faithful to it have zero Lebesgue measur...

Chain graphs present a broad class of graphical models for description of conditional independence structures, including both Markov networks and Bayesian networks as special cases. In this paper, we propose a computationally feasible method for the structural learning of chain graphs based on the idea of decomposing the learning problem into a set of smaller scale problems on its decomposed su...

In this paper we give a decomposition of a 4-connected graph G into nonseparating chains, which is similar to an ear decomposition of a 2-connected graph. We also give an O(|V (G)||E(G)|) algorithm that constructs such a decomposition. In applications, the asymptotic performance can often be improved to O(|V (G)|). This decomposition will be used to find four independent spanning trees in a 4co...

Probabilistic logics have attracted a great deal of attention during the past few years. While logical languages have taken a central position in research on knowledge representation and automated reasoning, probabilistic graphical models with their probabilistic basis have taken up a similar position when it comes to reasoning with uncertainty. The formalism of chain graphs is increasingly see...

The class of chain graphs (CGs) involving both undirected graphs (= Markov networks) and directed acyclic graphs (= Bayesian networks) was introduced in middle eighties for description of probabilistic conditional independence structures. Every class of Markov equivalent CGs (that is CGs describing the same conditional independence structure) has a natural representative, which is called the la...

4 A 3-connected graph is 3-connected if it has no 3-separation that separates a “large” fan or K3,n 5 from the rest of the graph. It is proved in this paper that, except for K4, every 3 -connected graph has 6 a 3-connected proper minor that is at most two edges away from the original graph. This result is used 7 to characterize Q-minor-free graphs, where Q is obtained from the Cube by contracti...