Institute of Information Theory and Automation

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Bibliography

Journal Article

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

Vomlel Jiří

: Kybernetika vol.47, 3 (2011), p. 317-336

: CEZ:AV0Z10750506

: 1M0572, GA MŠk, GA201/09/1891, GA ČR, 2C06019, GA MŠk, GEICC/08/E010, GA ČR

: Bayesian network, probabilistic inference, tensor rank

: http://library.utia.cas.cz/separaty/2011/MTR/vomlel-0361630.pdf

(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.

: BB

2019-01-07 08:39