Identifying the irreducible disjoint factors of a multivariate probability distribution

Maxime Gasse, Alex Aussem
Proceedings of the Eighth International Conference on Probabilistic Graphical Models, PMLR 52:183-194, 2016.

Abstract

We study the problem of decomposing a multivariate probability distribution p(\mathbfv) defined over a set of random variables \mathbfV={V_1,…,V_n} into a product of factors defined over disjoint subsets {\mathbfV_F_1,…,\mathbfV_F_m}. We show that the decomposition of \mathbfV 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 (V_i\perp V_j \mathbin∣\mathbfZ) under much less restrictive assumptions: 1) p supports the Intersection property ii) p supports the Composition property iii) no assumption at all.

Cite this Paper

BibTeX
@InProceedings{pmlr-v52-gasse16, title = {Identifying the irreducible disjoint factors of a multivariate probability distribution}, author = {Gasse, Maxime and Aussem, Alex}, booktitle = {Proceedings of the Eighth International Conference on Probabilistic Graphical Models}, pages = {183--194}, year = {2016}, editor = {Antonucci, Alessandro and Corani, Giorgio and Campos}, Cassio Polpo}, volume = {52}, series = {Proceedings of Machine Learning Research}, address = {Lugano, Switzerland}, month = {06--09 Sep}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v52/gasse16.pdf}, url = {https://proceedings.mlr.press/v52/gasse16.html}, abstract = {We study the problem of decomposing a multivariate probability distribution p(\mathbfv) defined over a set of random variables \mathbfV={V_1,…,V_n} into a product of factors defined over disjoint subsets {\mathbfV_F_1,…,\mathbfV_F_m}. We show that the decomposition of \mathbfV 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 (V_i\perp V_j \mathbin∣\mathbfZ) under much less restrictive assumptions: 1) p supports the Intersection property ii) p supports the Composition property iii) no assumption at all.} }
Endnote
%0 Conference Paper %T Identifying the irreducible disjoint factors of a multivariate probability distribution %A Maxime Gasse %A Alex Aussem %B Proceedings of the Eighth International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2016 %E Alessandro Antonucci %E Giorgio Corani %E Cassio Polpo Campos} %F pmlr-v52-gasse16 %I PMLR %P 183--194 %U https://proceedings.mlr.press/v52/gasse16.html %V 52 %X We study the problem of decomposing a multivariate probability distribution p(\mathbfv) defined over a set of random variables \mathbfV={V_1,…,V_n} into a product of factors defined over disjoint subsets {\mathbfV_F_1,…,\mathbfV_F_m}. We show that the decomposition of \mathbfV 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 (V_i\perp V_j \mathbin∣\mathbfZ) under much less restrictive assumptions: 1) p supports the Intersection property ii) p supports the Composition property iii) no assumption at all.
RIS
TY - CPAPER TI - Identifying the irreducible disjoint factors of a multivariate probability distribution AU - Maxime Gasse AU - Alex Aussem BT - Proceedings of the Eighth International Conference on Probabilistic Graphical Models DA - 2016/08/15 ED - Alessandro Antonucci ED - Giorgio Corani ED - Cassio Polpo Campos} ID - pmlr-v52-gasse16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 52 SP - 183 EP - 194 L1 - http://proceedings.mlr.press/v52/gasse16.pdf UR - https://proceedings.mlr.press/v52/gasse16.html AB - We study the problem of decomposing a multivariate probability distribution p(\mathbfv) defined over a set of random variables \mathbfV={V_1,…,V_n} into a product of factors defined over disjoint subsets {\mathbfV_F_1,…,\mathbfV_F_m}. We show that the decomposition of \mathbfV 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 (V_i\perp V_j \mathbin∣\mathbfZ) under much less restrictive assumptions: 1) p supports the Intersection property ii) p supports the Composition property iii) no assumption at all. ER -
APA
Gasse, M. & Aussem, A.. (2016). Identifying the irreducible disjoint factors of a multivariate probability distribution. Proceedings of the Eighth International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 52:183-194 Available from https://proceedings.mlr.press/v52/gasse16.html.

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