Representations of Bayesian Networks by Low-Rank Models

0493355 20240111141006.020180917235959.9 Representations of Bayesian Networks by Low-Rank Models 12 s. C cav_un_epca*0493354Proceedings of Machine Learning ResearchProceedings of Machine Learning Research72463-472PrahaUTIA2018KratochvílVáclavStudenýMilan canonical polyadic tensor decomposition conditional probability tables marginal probability tables cav_un_auth*0101212 Tichavský Petr Stochastická informatika Department of Stochastic Informatics SI SI UTIA-B Department of Stochastic Informatics Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0101228 Vomlel Jiří Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2018/SI/tichavsky-0493355.pdf 326 kB GA17-00902S GA ČR cav_un_auth*0345929 Conditional probability tables (CPTs) of discrete valued random variables may achieve high dimensions and Bayesian networks deﬁned as the product of these CPTs may become intractable by conventional methods of BN inference because of their dimensionality. In many cases, however, these probability tables constitute tensors of relatively low rank. Such tensors can be written in the so-called Kruskal form as a sum of rank-one components. Such representation would be equivalent to adding one artiﬁcial parent to all random variables and deleting all edges between the variables. The most difﬁcult task is to ﬁnd such a representation given a set of marginals or CPTs of the random variables under consideration. In the former case, it is a problem of joint canonical polyadic (CP) decomposition of a set of tensors. The latter ﬁtting problem can be solved in a similar manner. We apply a recently proposed alternating direction method of multipliers (ADMM), which assures that the model has a probabilistic interpretation, i.e., that all elements of all factor matrices are nonnegative. We perform experiments with several well-known Bayesian networks. cav_un_auth*0363930 International Conference on Probabilistic Graphical Models 20180911 20180914 Praha CZ BA 10000 10100 10103 2019 2 PR RVO:67985556 http://hdl.handle.net/11104/0286997 S 2018 326 kB cav_un_epca*0493354 Proceedings of Machine Learning Research 72 UTIA 2018 Praha 463 472 1938-7228 340 Kratochvíl Václav 340 Studený Milan