# Bibliography

Journal Article

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

,

**: **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

**: **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