An Algebraic Implicitization and Specialization of Minimum KL-Divergence Models

  • Ambedkar Dukkipati
  • Joel George Manathara
Conference paper

DOI: 10.1007/978-3-642-15274-0_8

Volume 6244 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Dukkipati A., Manathara J.G. (2010) An Algebraic Implicitization and Specialization of Minimum KL-Divergence Models. In: Gerdt V.P., Koepf W., Mayr E.W., Vorozhtsov E.V. (eds) Computer Algebra in Scientific Computing. CASC 2010. Lecture Notes in Computer Science, vol 6244. Springer, Berlin, Heidelberg

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 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Ambedkar Dukkipati
    • 1
  • Joel George Manathara
    • 2
  1. 1.Department of Computer Science and AutomationIndian Institute of ScienceIndia
  2. 2.Department of Aerospace EngineeringIndian Institute of ScienceIndia