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Rank of tensors of l-out-of-k functions: an application in probabilistic inference

SYSNO ASEP	0361630
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Rank of tensors of l-out-of-k functions: an application in probabilistic inference
Author(s)	Vomlel, Jiří (UTIA-B)_{RID, ORCID}
Number of authors	1
Source Title	Kybernetika. - : Ústav teorie informace a automatizace AV ČR, v. v. i. - ISSN 0023-5954 Roč. 47, č. 3 (2011), s. 317-336
Number of pages	20 s.
Language	eng - English
Country	CZ - Czech Republic
Keywords	Bayesian network ; probabilistic inference ; tensor rank
Subject RIV	BB - Applied Statistics, Operational Research
R&D Projects	1M0572 GA MŠMT - Ministry of Education, Youth and Sports (MEYS)
	GA201/09/1891 GA ČR - Czech Science Foundation (CSF)
	GEICC/08/E010 GA ČR - Czech Science Foundation (CSF)
CEZ	AV0Z10750506 - UTIA-B (2005-2011)
UT WOS	000293207900002
EID SCOPUS	83455262599
Annotation	We study the problem of efficient probabilistic inference with Bayesian networks when some of the conditional probability tables represent deterministic or noisy l-out-of-k functions. These tables appear naturally in real-world applications when we observe a state of a variable that depends on its parents via an addition or noisy addition relation. We provide a lower bound of the rank and an upper bound for the symmetric border rank of tensors representing l-out-of-k functions. We propose an approximation of tensors representing noisy l-out-of-k functions by a sum of r tensors of rank one, where r is an upper bound of the symmetric border rank of the approximated tensor. We applied the suggested approximation to probabilistic inference in probabilistic graphical models. Numerical experiments reveal that we can get a gain in the order of two magnitudes but at the expense of a certain loss of precision.
Workplace	Institute of Information Theory and Automation
Contact	Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201.
Year of Publishing	2012

Number of the records: 1