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Identifying the irreducible disjoint factors of a multivariate probability distribution.

Maxime Gasse 1 Alex Aussem 1 
1 DM2L - Data Mining and Machine Learning
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
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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Contributor : Maxime Gasse Connect in order to contact the contributor
Submitted on : Tuesday, January 3, 2017 - 3:35:21 PM
Last modification on : Friday, September 30, 2022 - 11:34:16 AM
Long-term archiving on: : Tuesday, April 4, 2017 - 2:30:14 PM


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  • HAL Id : hal-01425447, version 1


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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