KYBERNETIKA

Kybernetika 45(2):189-207, 2009.

Hierarchical Models, Marginal Polytopes, and Linear Codes

Thomas Kahle, Walter Wenzel and Nihat Ay

Abstract:

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.

Keywords: 0/1 polytopes; linear codes; hierarchical models; exponential families;

AMS: 52B11; 94B05; 60C05;