Embedding maximum entropy models in algebraic varieties by Gröbner bases methods

Abstract

The main aim of this paper is to present some notions on how results from commutative algebra and algebraic geometry could be used in representation and computation of maximum entropy (ME) models in the cases, where an integer valued sufficient statistic exists. We give an implicit description of ME-models by embedding them in algebraic varieties for which we use Gröbner bases methods. We prove that in the case of ME, both the model and the data can be represented by algebraic varieties.