bibtype	J - Journal Article
ARLID	0361630
utime	20240903170623.4
mtime	20110913235959.9
WOS	000293207900002
SCOPUS	83455262599
title (primary) (eng)	Rank of tensors of l-out-of-k functions: an application in probabilistic inference
specification	page_count 20 s.
serial	ARLID cav_un_epca*0297163 ISSN 0023-5954 title Kybernetika volume_id 47 volume 3 (2011) page_num 317-336 publisher name Ústav teorie informace a automatizace AV ČR, v. v. i.
keyword	Bayesian network
keyword	probabilistic inference
keyword	tensor rank
author (primary)	ARLID cav_un_auth*0101228 name1 Vomlel name2 Jiří full_dept (cz) Matematická teorie rozhodování full_dept (eng) Department of Decision Making Theory department (cz) MTR department (eng) MTR institution UTIA-B full_dept Department of Decision Making Theory fullinstit Ústav teorie informace a automatizace AV ČR, v. v. i.
source	url http://library.utia.cas.cz/separaty/2011/MTR/vomlel-0361630.pdf
cas_special	project project_id 1M0572 agency GA MŠk ARLID cav_un_auth*0001814 project project_id GA201/09/1891 agency GA ČR ARLID cav_un_auth*0253175 project project_id 2C06019 agency GA MŠk country CZ ARLID cav_un_auth*0216518 project project_id GEICC/08/E010 agency GA ČR ARLID cav_un_auth*0241637 research CEZ:AV0Z10750506 abstract (eng) 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. reportyear 2012 RIV BB num_of_auth 1 mrcbC52 4 A O 4a 4o 20231122134625.5 permalink http://hdl.handle.net/11104/0198901 mrcbT16-e COMPUTERSCIENCECYBERNETICS mrcbT16-f 0.473 mrcbT16-g 0.033 mrcbT16-h 9.5 mrcbT16-i 0.0016 mrcbT16-j 0.277 mrcbT16-k 403 mrcbT16-l 61 mrcbT16-q 21 mrcbT16-s 0.307 mrcbT16-y 20.45 mrcbT16-x 0.61 mrcbT16-4 Q2 mrcbT16-B 23.915 mrcbT16-C 17.500 mrcbT16-D Q4 mrcbT16-E Q3 arlyear 2011 mrcbTft \nSoubory v repozitáři: vomlel-0361630.pdf, 0361630.pdf mrcbU14 83455262599 SCOPUS mrcbU34 000293207900002 WOS mrcbU63 cav_un_epca*0297163 Kybernetika 0023-5954 Roč. 47 č. 3 2011 317 336 Ústav teorie informace a automatizace AV ČR, v. v. i.