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

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About: Rank of tensors of l-out-of-k functions: an application in probabilistic inference Goto Sponge NotDistinct Permalink

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	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. 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. (en)
Title	Rank of tensors of l-out-of-k functions: an application in probabilistic inference Rank of tensors of l-out-of-k functions: an application in probabilistic inference (en)
skos:prefLabel	Rank of tensors of l-out-of-k functions: an application in probabilistic inference Rank of tensors of l-out-of-k functions: an application in probabilistic inference (en)
skos:notation	RIV/67985556:_____/11:00361630!RIV12-AV0-67985556
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(1M0572), P(2C06019), P(GA201/09/1891), P(GEICC/08/E010), Z(AV0Z10750506)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Vomlel, Jiří
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav teorie informace a automatizace AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	225694
http://linked.open...ai/riv/idVysledku	RIV/67985556:_____/11:00361630
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Bayesian network; probabilistic inference; tensor rank (en)
http://linked.open.../riv/klicoveSlovo	Bayesian network probabilistic inference tensor rank
http://linked.open...odStatuVydavatele	CZ - Česká republika
http://linked.open...ontrolniKodProRIV	[9315F5B0C1F8]
http://linked.open...i/riv/nazevZdroje	Kybernetika
http://linked.open...in/vavai/riv/obor	BB
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Data, algorithms, decision making (Medical) Knowledge Acquisition and Modelling Multidimensional Models of Uncertainty The logic of causal and probabilistic reasoning in uncertain environments
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	47
http://linked.open...iv/tvurceVysledku	Vomlel, Jiří
http://linked.open...ain/vavai/riv/wos	000293207900002
http://linked.open...n/vavai/riv/zamer	Pokročilé matematické metody získávání, zpracování a využití informací a znalostí ve složitých a nedeterministických systémech
issn	0023-5954
number of pages	20 (xsd:int)

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