Logical Inference Algorithms and Matrix Representations for Probabilistic Conditional Independence
Logical inference algorithms for conditional independence (CI) statements have important applications from testing consistency during knowledge elicitation to constraintbased 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.
PDF Link: /papers/09/p428-niepert.pdf
AUTHOR = "Mathias Niepert
TITLE = "Logical Inference Algorithms and Matrix Representations for Probabilistic Conditional Independence",
BOOKTITLE = "Proceedings of the Twenty-Fifth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-09)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2009",
PAGES = "428--435"