Generalized Permutohedra from Probabilistic Graphical Models

Faces of Generalized Permutohedra

The aim of the paper is to calculate face numbers of simple generalized permutohedra, and study their f -, hand γvectors. These polytopes include permutohedra, associahedra, graphassociahedra, simple graphic zonotopes, nestohedra, and other interesting polytopes. We give several explicit formulas for h-vectors and γ-vectors involving descent statistics. This includes a combinatorial interpretat...

Probabilistic Graphical Models

P Probabilistic Graphical Models

Bayesian network (BN) A directed graph whose nodes represent variables, and edges represent influences. Together with conditional probability distributions, a Bayesian network represents the joint probability distribution of its variables. Conditional probability distribution Assignment of probabilities to all instances of a set of variables when the value of one or more variables is known. Con...

Visualizing Graphical Probabilistic Models

Complex probabilistic models are difficult to evaluate not only for consistency with the domain theory but also for novelty and significance. In this paper we describe the current visual representations of Bayesian networks and then present an implementation containing enhancements to these visualizations by integrating several well known techniques. We then apply our approach in an exploration...

Probabilistic Graphical Models

This report1 presents probabilistic graphical models that are based on imprecise probabilities using a comprehensive language. In particular, the discussion is focused on credal networks and discrete domains. It describes the building blocks of credal networks, algorithms to perform inference, and discusses on complexity results and related work. The goal is to present an easy-to-follow introdu...