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.
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01425447
Contributor : Maxime Gasse <>
Submitted on : Tuesday, January 3, 2017 - 3:35:21 PM
Last modification on : Thursday, November 21, 2019 - 2:37:58 AM
Long-term archiving on : Tuesday, April 4, 2017 - 2:30:14 PM

File

gasse16.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01425447, version 1

Citation

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⟩

Share

Metrics

Record views

614

Files downloads

228