0361630 20240903170623.420110913235959.9 000293207900002 83455262599 20 s. cav_un_epca*02971630023-5954473 (2011)317-336Ústav teorie informace a automatizace AV ČR, v. v. i. Bayesian network probabilistic inference tensor rank cav_un_auth*0101228 Vomlel Jiří Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2011/MTR/vomlel-0361630.pdf 1M0572 GA MŠk cav_un_auth*0001814 GA201/09/1891 GA ČR cav_un_auth*0253175 2C06019 GA MŠk CZ cav_un_auth*0216518 GEICC/08/E010 GA ČR cav_un_auth*0241637 CEZ:AV0Z10750506 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. 2012 BB 1 4 A O 4a 4o 20231122134625.5 http://hdl.handle.net/11104/0198901 COMPUTERSCIENCECYBERNETICS 0.473 0.033 9.5 0.0016 0.277 403 61 21 0.307 20.45 0.61 Q2 23.915 17.500 Q4 Q3 2011 Soubory v repozitáři: vomlel-0361630.pdf, 0361630.pdf 83455262599 SCOPUS 000293207900002 WOS cav_un_epca*0297163 Kybernetika 0023-5954 Roč. 47 č. 3 2011 317 336 Ústav teorie informace a automatizace AV ČR, v. v. i.