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Journal Article

Probabilistic inference with noisy-threshold models based on a CP tensor decomposition

Vomlel Jiří, Tichavský Petr

: International Journal of Approximate Reasoning vol.55, 4 (2014), p. 1072-1092

: GA13-20012S, GA ČR, GA102/09/1278, GA ČR

: Bayesian networks, Probabilistic inference, Candecomp-Parafac tensor decomposition, Symmetric tensor rank

: 10.1016/j.ijar.2013.12.002

: http://library.utia.cas.cz/separaty/2014/MTR/vomlel-0427059.pdf

(eng): The specification of conditional probability tables (CPTs) is a difficult task in the construction of probabilistic graphical models. Several types of canonical models have been proposed to ease that difficulty. Noisy-threshold models generalize the two most popular canonical models: the noisy-or and the noisy-and. When using the standard inference techniques the inference complexity is exponential with respect to the number of parents of a variable. More efficient inference techniques can be employed for CPTs that take a special form. CPTs can be viewed as tensors. Tensors can be decomposed into linear combinations of rank-one tensors, where a rank-one tensor is an outer product of vectors. Such decomposition is referred to as Canonical Polyadic (CP) or CANDECOMP-PARAFAC (CP) decomposition. The tensor decomposition offers a compact representation of CPTs which can be efficiently utilized in probabilistic inference.

: JD