An algebraic implicitization and specialization of minimum KL-divergence models

Authors:
Ambedkar Dukkipati;Joel George Manathara
Affiliations:
Department of Computer Science and Automation, Indian Institute of Science, Bangalore, India;Department of Aerospace Engineering, Indian Institute of Science, Bangalore, India
Venue:
CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
Year:
2010

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Abstract

In this paper we study representation of KL-divergence minimization, in the cases where integer sufficient statistics exists, using tools from polynomial algebra. We show that the estimation of parametric statistical models in this case can be transformed to solving a system of polynomial equations. In particular, we also study the case of Kullback-Csiszar iteration scheme. We present implicit descriptions of these models and show that implicitization preserves specialization of prior distribution. This result leads us to a Gröbner bases method to compute an implicit representation of minimum KL-divergence models.