Chapter

Computer Algebra in Scientific Computing

Volume 6244 of the series Lecture Notes in Computer Science pp 85-96

An Algebraic Implicitization and Specialization of Minimum KL-Divergence Models

  • Ambedkar DukkipatiAffiliated withCarnegie Mellon UniversityDepartment of Computer Science and Automation, Indian Institute of Science
  • , Joel George ManatharaAffiliated withCarnegie Mellon UniversityDepartment of Aerospace Engineering, Indian Institute of Science

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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-Csisźar 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.

Keywords

Gröbner Bases statistical models elimination