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.
Type de document :
Communication dans un congrès
Alessandro Antonucci; Giorgio Corani; Cassio Polpo de Campos. Probabilistic Graphical Models, Sep 2016, Lugano, Switzerland. JMLR.org, JMLR Workshop and Conference Proceedings, 52, pp.183 - 194, 2016, Proceedings of the Eighth International Conference on Probabilistic Graphical Models. 〈http://jmlr.org/proceedings/papers/v52/〉
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Soumis le : mardi 3 janvier 2017 - 15:35:21
Dernière modification le : jeudi 8 février 2018 - 11:10:31
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Maxime Gasse, Alex Aussem. Identifying the irreducible disjoint factors of a multivariate probability distribution.. Alessandro Antonucci; Giorgio Corani; Cassio Polpo de Campos. Probabilistic Graphical Models, Sep 2016, Lugano, Switzerland. JMLR.org, JMLR Workshop and Conference Proceedings, 52, pp.183 - 194, 2016, Proceedings of the Eighth International Conference on Probabilistic Graphical Models. 〈http://jmlr.org/proceedings/papers/v52/〉. 〈hal-01425447〉

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