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On solution sets of information inequalities

Nihat Ay;  Walter Wenzel — 2012

Kybernetika

We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce structural properties of Bayesian networks, which is important within causal inference.

Hierarchical models, marginal polytopes, and linear codes

Thomas Kahle;  Walter Wenzel;  Nihat Ay — 2009

Kybernetika

In this paper, we explore a connection between binary hierarchical models, their marginal polytopes, and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is determined. We classify all full dimensional polytopes with the property that their vertices form a linear code and give an algorithm that determines them.

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