Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
A munin network for the median nerve-a case study on loops
Applied Artificial Intelligence
Decision-theoretic troubleshooting
Communications of the ACM
Decomposition of quantics in sums of powers of linear forms
Signal Processing - Special issue on higher order statistics
An introduction to variational methods for graphical models
Learning in graphical models
LAZY propagation: a junction tree inference algorithm based on lazy evaluation
Artificial Intelligence
Bayesian Networks and Decision Graphs
Bayesian Networks and Decision Graphs
A Tractable Inference Algorithm for Diagnosing Multiple Diseases
UAI '89 Proceedings of the Fifth Annual Conference on Uncertainty in Artificial Intelligence
A differential approach to inference in Bayesian networks
Journal of the ACM (JACM)
The SACSO methodology for troubleshooting complex systems
Artificial Intelligence for Engineering Design, Analysis and Manufacturing
Predicting carcinoid heart disease with the noisy-threshold classifier
Artificial Intelligence in Medicine
On probabilistic inference by weighted model counting
Artificial Intelligence
Learning symmetric causal independence models
Machine Learning
Symmetric Tensors and Symmetric Tensor Rank
SIAM Journal on Matrix Analysis and Applications
Bayesian Networks and Decision Graphs
Bayesian Networks and Decision Graphs
Modelling treatment effects in a clinical Bayesian network using Boolean threshold functions
Artificial Intelligence in Medicine
Performing Bayesian inference by weighted model counting
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Exploiting causal independence in Bayesian network inference
Journal of Artificial Intelligence Research
Compiling Bayesian networks with local structure
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Approximate inference in Bayesian networks using binary probability trees
International Journal of Approximate Reasoning
Exploiting structure in weighted model counting approaches to probabilistic inference
Journal of Artificial Intelligence Research
Multiplicative factorization of noisy-max
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Context-specific independence in Bayesian networks
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
A new look at causal independence
UAI'94 Proceedings of the Tenth international conference on Uncertainty in artificial intelligence
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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. In this paper we propose a CP decomposition of tensors corresponding to CPTs of threshold functions, exactly @?-out-of-k functions, and their noisy counterparts. We prove results about the symmetric rank of these tensors in the real and complex domains. The proofs are constructive and provide methods for CP decomposition of these tensors. An analytical and experimental comparison with the parent-divorcing method (which also has a polynomial complexity) shows superiority of the CP decomposition-based method. The experiments were performed on subnetworks of the well-known QMRT-DT network generalized by replacing noisy-or by noisy-threshold models.