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Representations of Bayesian Networks by Low-Rank Models
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SYSNO ASEP 0493355 Druh ASEP K - Konferenční příspěvek (lokální konf.) Zařazení RIV Stať ve sborníku Název Representations of Bayesian Networks by Low-Rank Models Tvůrce(i) Tichavský, Petr (UTIA-B) RID, ORCID
Vomlel, Jiří (UTIA-B) RID, ORCIDCelkový počet autorů 2 Zdroj.dok. Proceedings of Machine Learning Research, 72. - Praha : UTIA, 2018 / Kratochvíl Václav ; Studený Milan
S. 463-472Poč.str. 12 s. Forma vydání Nosič - C Akce International Conference on Probabilistic Graphical Models Datum konání 11.09.2018 - 14.09.2018 Místo konání Praha Země CZ - Česká republika Typ akce WRD Jazyk dok. eng - angličtina Země vyd. CZ - Česká republika Klíč. slova canonical polyadic tensor decomposition ; conditional probability tables ; marginal probability tables Vědní obor RIV BA - Obecná matematika Obor OECD Statistics and probability CEP GA17-00902S GA ČR - Grantová agentura ČR Institucionální podpora UTIA-B - RVO:67985556 Anotace 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.
Pracoviště Ústav teorie informace a automatizace Kontakt Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Rok sběru 2019
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