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Representations of Bayesian Networks by Low-Rank Models
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SYSNO ASEP 0493355 Document Type K - Proceedings Paper (Czech conf.) R&D Document Type Conference Paper Title Representations of Bayesian Networks by Low-Rank Models Author(s) Tichavský, Petr (UTIA-B) RID, ORCID
Vomlel, Jiří (UTIA-B) RID, ORCIDNumber of authors 2 Source Title Proceedings of Machine Learning Research, 72. - Praha : UTIA, 2018 / Kratochvíl Václav ; Studený Milan
S. 463-472Number of pages 12 s. Publication form Medium - C Action International Conference on Probabilistic Graphical Models Event date 11.09.2018 - 14.09.2018 VEvent location Praha Country CZ - Czech Republic Event type WRD Language eng - English Country CZ - Czech Republic Keywords canonical polyadic tensor decomposition ; conditional probability tables ; marginal probability tables Subject RIV BA - General Mathematics OECD category Statistics and probability R&D Projects GA17-00902S GA ČR - Czech Science Foundation (CSF) Institutional support UTIA-B - RVO:67985556 Annotation 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.
Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2019
Number of the records: 1