Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Constraint Processing
Stable independence and complexity of representation
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Probabilistic Conditional Independence Structures: With 42 Illustrations (Information Science and Statistics)
Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Racing algorithms for conditional independence inference
International Journal of Approximate Reasoning
Three counter-examples on semi-graphoids
Combinatorics, Probability and Computing
Elicitation of probabilities for belief networks: combining qualitative and quantitative information
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Logical and algorithmic properties of stable conditional independence
International Journal of Approximate Reasoning
Efficient Algorithms for Conditional Independence Inference
The Journal of Machine Learning Research
Characteristic imsets for learning Bayesian network structure
International Journal of Approximate Reasoning
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Logical inference algorithms for conditional independence (CI) statements have important applications from testing consistency during knowledge elicitation to constraint-based structure learning of graphical models. We prove that the implication problem for CI statements is decidable, given that the size of the domains of the random variables is known and fixed. We will present an approximate logical inference algorithm which combines a falsification and a novel validation algorithm. The validation algorithm represents each set of CI statements as a sparse 0--1 matrix A and validates instances of the implication problem by solving specific linear programs with constraint matrix A. We will show experimentally that the algorithm is both effective and efficient in validating and falsifying instances of the probabilistic CI implication problem.