Artificial Intelligence
Probabilistic reasoning using graphs
Processing and Management of Uncertainty in Knowledge-Based Systems on Uncertainty in knowledge-based systems. International Conference on Information
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Modeling probabilistic networks of discrete and continuous variables
Journal of Multivariate Analysis
Bayesian Networks and Decision Graphs
Bayesian Networks and Decision Graphs
Dependency networks for inference, collaborative filtering, and data visualization
The Journal of Machine Learning Research
Learning Bayesian Networks
Uncertainty, belief, and probability
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
Evolved artificial signalling networks for the control of a conservative complex dynamical system
IPCAT'12 Proceedings of the 9th international conference on Information Processing in Cells and Tissues
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Although undirected cycles in directed graphs of Bayesian belief networks have been thoroughly studied, little attention has so far been given to a systematic analysis of directed (feedback) cycles. In this paper we propose a way of looking at those cycles; namely, we suggest that a feedback cycle represents a family of probabilistic distributions rather than a single distribution (as a regular Bayesian belief network does). A non-empty family of distributions can be explicitly represented by an ideal of conjunctions with interval estimates on the probabilities of its elements. This ideal can serve as a probabilistic model of an expert's uncertain knowledge pattern; such models are studied in the theory of algebraic Bayesian networks. The family of probabilistic distributions may also be empty; in this case, the probabilistic assignment over cycle nodes is inconsistent. We propose a simple way of explicating the probabilistic relationships an isolated directed cycle contains, give an algorithm (based on linear programming) of its consistency checking, and establish a lower bound of the complexity of this checking.