Identifying the Irreducible Disjoint Factors of a Multivariate Probability Distribution
Abstract
We study the problem of decomposing a multivariate probability distribution p(\mathbf{v}) defined over a set of random variables \mathbf{V}=V_1,…,V_n into a product of factors defined over disjoint subsets {\mathbf{V_F_1},…,\mathbf{V_F_m}}. We show that the decomposition of \mathbf{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 (V_i\perp V_j \mathbin∣\mathbf{Z}) under much less restrictive assumptions: 1) p supports the Intersection property ii) p supports the Composition property iii) no assumption at all.
Cite
Text
Gasse and Aussem. "Identifying the Irreducible Disjoint Factors of a Multivariate Probability Distribution." Proceedings of the Eighth International Conference on Probabilistic Graphical Models, 2016.Markdown
[Gasse and Aussem. "Identifying the Irreducible Disjoint Factors of a Multivariate Probability Distribution." Proceedings of the Eighth International Conference on Probabilistic Graphical Models, 2016.](https://mlanthology.org/pgm/2016/gasse2016pgm-identifying/)BibTeX
@inproceedings{gasse2016pgm-identifying,
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},
year = {2016},
pages = {183-194},
volume = {52},
url = {https://mlanthology.org/pgm/2016/gasse2016pgm-identifying/}
}