Marginal AMP chain graphs are a recently introduced family of models that is based on graphs that may have undirected, directed and bidirected edges. They unify and generalize the AMP and the multivariate regression interpretations of chain graphs. In this paper, we present a constraint based algorithm for learning a marginal AMP chain graph from a probability distribution which is faithful to ...

Chain graphs combine directed and undi­ rected graphs and their underlying mathe­ matics combines properties of the two. This paper gives a simplified definition of chain graphs based on a hierarchical combination of Bayesian (directed) and Markov (undirected) networks. Examples of a chain graph are multivariate feed-forward networks, cluster­ ing with conditional interaction between vari­ able...

Intelligent systems require software incorporating probabilistic reasoning, and often times learning. Networks provide a framework and methodology for creating this kind of software. This paper introduces network models based on chain graphs with deter-ministic nodes. Chain graphs are deened as a hierarchical combination of Bayesian and Markov networks. To model learning, plates on chain graphs...

In this article we study the expressiveness of the different chain graph interpretations. Chain graphs is a class of probabilistic graphical models that can contain two types of edges, representing different types of relationships between the variables in question. Chain graphs is also a superclass of directed acyclic graphs, i.e. Bayesian networks, and can thereby represent systems more accura...

Jacobson, MS., J. Lehel and L.M. Lesniak, @threshold and $-tolerance chain graphs, Discrete Applied Mathematics 44 (1993) 191-203. In this paper we introduce a class of graphs called $-threshold graphs which generalize threshold graphs. These graphs are studied for various functions I+? that include “max” and “min” as special cases. The graphs are then shown to fit into the more general setting...

Probabilistic graphical models are currently one of the most commonly used architectures for modelling and reasoning with uncertainty. The most widely used subclass of these models is directed acyclic graphs, also known as Bayesian networks, which are used in a wide range of applications both in research and industry. Directed acyclic graphs do, however, have a major limitation, which is that o...

Any regular Gaussian probability distribution that can be represented by an AMP chain graph (CG) can be expressed as a system of linear equations with correlated errors whose structure depends on the CG. However, the CG represents the errors implicitly, as no nodes in the CG correspond to the errors. We propose in this paper to add some deterministic nodes to the CG in order to represent the er...

One of the most common ways of representing classes of equivalent Bayesian networks is the use of essential graphs. These chain graphs are also known in the literature as completed patterns or completed pdags. The name essential graph was proposed by Andersson, Madigan and Perlman (1997a) who also gave a graphical characterization of essential graphs. In this contribution an alternative charact...

Essential graphs and largest chain graphs are well-established graphical representations of equivalence classes of DAGs and chain graphs (CGs) respectively, especially useful in the context of structural learning. Recently, Roverato and La Rocca (2004) introduced the notion of a labelled block ordering of vertices B as a flexible tool for specifying subfamilies of CGs. In particular, both the f...