Neighborliness of Marginal Polytopes

Abstract

A neighborliness property of marginal polytopes of hierarchical models, depending on the cardinality of the smallest non-face of the underlying simplicial complex, is shown. The case of binary variables is studied explicitly, then the general case is reduced to the binary case. A Markov basis for binary hierarchical models whose simplicial complexes is the complement of an interval is given.

9 pages

References in corpus (3)

• On the toric algebra of graphical models
• Complexity Measures from Interaction Structures
• Maximizing Multi-Information

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