Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Conditional independence structures examined via minors
Annals of Mathematics and Artificial Intelligence
On characterization of entropy function via information inequalities
IEEE Transactions on Information Theory
Conditional independence structures examined via minors
Annals of Mathematics and Artificial Intelligence
On Stochastic Conditional Independence: the Problems of Characterization and Description
Annals of Mathematics and Artificial Intelligence
Three counter-examples on semi-graphoids
Combinatorics, Probability and Computing
Algebraic geometry of Bayesian networks
Journal of Symbolic Computation
Violating the Ingleton inequality with finite groups
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Conditional independences in gaussian vectors and rings of polynomials
WCII'02 Proceedings of the 2002 international conference on Conditionals, Information, and Inference
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The problem of probabilistic representability of semimatroids over a four-element set is solved. In this problem, one looks for all combinations of conditional independences within four random variables which can occur simultaneously. New properties of the stochastic conditional independences are deduced from conditional information inequalities. Examples of four-tuples of random variables are presented to show the probabilistic representability of three non-Ingleton semimatroids.