Parameter estimation and model selection for mixtures of truncated exponentials

  • Authors:

  • Helge Langseth;Thomas D. Nielsen;Rafael Rumı´;Antonio Salmerón

  • Affiliations:

  • Department of Computer and Information Science, The Norwegian University of Science and Technology, Trondheim, Norway;Department of Computer Science, Aalborg University, Aalborg, Denmark;Department of Statistics and Applied Mathematics, University of Almerı´a, Almerı´a, Spain;Department of Statistics and Applied Mathematics, University of Almerı´a, Almerı´a, Spain

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2010

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Abstract

Bayesian networks with mixtures of truncated exponentials (MTEs) support efficient inference algorithms and provide a flexible way of modeling hybrid domains (domains containing both discrete and continuous variables). On the other hand, estimating an MTE from data has turned out to be a difficult task, and most prevalent learning methods treat parameter estimation as a regression problem. The drawback of this approach is that by not directly attempting to find the parameter estimates that maximize the likelihood, there is no principled way of performing subsequent model selection using those parameter estimates. In this paper we describe an estimation method that directly aims at learning the parameters of an MTE potential following a maximum likelihood approach. Empirical results demonstrate that the proposed method yields significantly better likelihood results than existing regression-based methods. We also show how model selection, which in the case of univariate MTEs amounts to partitioning the domain and selecting the number of exponential terms, can be performed using the BIC score.