Rank of tensor of ℓ-out-of-k functions: an appplication in probabilistic inference

Title:

Rank of tensor of ℓ-out-of-k functions: an appplication in probabilistic inference

Creator:

Vomlel, Jiří

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:43d4526f-bb26-4c3d-9f03-b5a12cd800bf
uuid:43d4526f-bb26-4c3d-9f03-b5a12cd800bf

Subject:

Bayesian networks, probabilistic inference, uncertainty in artificial inteligence, tensor rank, symmetric rank, and border ank

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Bayesian networks are a popular model for reasoning under uncertainty. We study the problem of efficient probabilistic inference with these models 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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[317]-336

Source:

Kybernetika | 2011 Volume:47 | Number:3

Harvested from:

CDK

Metadata only:

false