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

0361630 - ÚTIA 2012 RIV CZ eng J - Článek v odborném periodiku
Vomlel, Jiří
Rank of tensors of l-out-of-k functions: an application in probabilistic inference.
Kybernetika. Roč. 47, č. 3 (2011), s. 317-336. ISSN 0023-5954
Grant CEP: GA MŠMT 1M0572; GA ČR GA201/09/1891; GA ČR GEICC/08/E010
Grant ostatní: GA MŠk(CZ) 2C06019
Výzkumný záměr: CEZ:AV0Z10750506
Klíčová slova: Bayesian network * probabilistic inference * tensor rank
Kód oboru RIV: BB - Aplikovaná statistika, operační výzkum
Impakt faktor: 0.454, rok: 2011
http://library.utia.cas.cz/separaty/2011/MTR/vomlel-0361630.pdf

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.
Trvalý link: http://hdl.handle.net/11104/0198901