As a reaction to the restrictive Gaussian assumptions that are usually part of graphical models, Vogel and Fried [17] recently introduced elliptical graphical models, in which the vector of variables at hand is assumed to have an elliptical distribution. The present work introduces a class of...

This paper deals with the Bayesian analysis of graphical models of marginal independence for three way contingency tables. Each marginal independence model corresponds to a particular factorization of the cell probabilities and a conjugate analysis based on Dirichlet prior can be performed. We...

Let (omega,F,P) be a probability space. For each G in F, define G as the s-field generated by G and those sets f in F satisfying P(f) in {0, 1}. Conditions for P to be atomic on the intersection of the complements of Ai for i=1,..,k, with A1, . . . ,Ak in F sub-s-fields, are given. Conditions...

Abstract In this article, we propose a new method to learn the underlying acyclic mixed graph of a linear non-Gaussian structural equation model with given observational data. We build on an algorithm proposed by Wang and Drton, and we show that one can augment the hidden variable structure of...

Abstract I thank Ilya Shpitser for his comments on my article, and discuss the use of models with restricted interventions.

This report introduces a novel approach to performing inference and learning in Dynamic Bayesian Networks (DBN). The traditional approach to inference and learning in DBNs involves conditioning on one or more finite-length observation sequences. In this report, we consider conditioning on what...

Conference Paper

Probabilistic graphical models, by making conditional independence assumptions, can represent complex joint distributions in a factorized form. However, in large problems graphical models often run into two issues. First, in non-treelike graphs, computational issues frustrate exact inference....

This thesis presents a class of graphical models for directly representing the joint cumulative distribution function (CDF) of many random variables, called cumulative distribution networks (CDNs). Unlike graphical models for probability density and mass functions, in a CDN, the marginal...