Perfect Tree-Like Markovian Distributions

2013/01/16 by Ann Becker, Becker, Ann, Dan Geiger +3
Computer Science · Decision Sciences · #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #Data Management and Algorithms #FOS: Computer and information sciences #Multi-Criteria Decision Making #cs.AI

paper · pdf · doi:10.48550/arxiv.1301.3834

Appears in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI2000)

arxiv created 2013/01/16 · openalex publication_date 2013/01/16 · arxiv updated 2013/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if a strictly positive joint probability distribution for a set of binary random variables factors according to a tree, then vertex separation represents all and only the independence relations enclosed in the distribution. The same result is shown to hold also for multivariate strictly positive normal distributions. Our proof uses a new property of conditional independence that holds for these two classes of probability distributions.

Cited by

• Multiple Testing and Error Control in Gaussian Graphical Model Selection
• Detection of Unfaithfulness and Robust Causal Inference
• Geometry of the faithfulness assumption in causal inference

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