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Conference Papers Year : 2016

Identifying the irreducible disjoint factors of a multivariate probability distribution.

Maxime Gasse
Alex Aussem

Abstract

We study the problem of decomposing a multivariate probability distribution p(v) defined over a set of random variables V = {V1 ,. .. , Vn } into a product of factors defined over disjoint subsets {VF1 ,. .. , VFm }. We show that the decomposition of V into irreducible disjoint factors forms a unique partition, which corresponds to the connected components of a Bayesian or Markov network , given that it is faithful to p. Finally, we provide three generic procedures to identify these factors with O(n^2) pairwise conditional independence tests (Vi ⊥ Vj |Z) under much less restrictive assumptions: 1) p supports the Intersection property; ii) p supports the Composition property; iii) no assumption at all.
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Dates and versions

hal-01425447 , version 1 (03-01-2017)

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  • HAL Id : hal-01425447 , version 1

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Maxime Gasse, Alex Aussem. Identifying the irreducible disjoint factors of a multivariate probability distribution.. Probabilistic Graphical Models, Sep 2016, Lugano, Switzerland. pp.183 - 194. ⟨hal-01425447⟩
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