Irrelevance and Independence Relations in Quasi-Bayesian Networks
This work addresses foundational issues in uncertainty modeling for researchers in probabilistic graphical models and imprecise probability, but it appears incremental as it builds on existing Walley's definitions and d-separation concepts.
The paper tackles the problem of detecting, enforcing, and exploiting irrelevance and independence relations in Quasi-Bayesian networks, which are graphical models based on convex sets of probability distributions, by presenting novel algorithms and results for inferences using fractional linear programming and clarifying properties through a new generalization of d-separation.
This paper analyzes irrelevance and independence relations in graphical models associated with convex sets of probability distributions (called Quasi-Bayesian networks). The basic question in Quasi-Bayesian networks is, How can irrelevance/independence relations in Quasi-Bayesian networks be detected, enforced and exploited? This paper addresses these questions through Walley's definitions of irrelevance and independence. Novel algorithms and results are presented for inferences with the so-called natural extensions using fractional linear programming, and the properties of the so-called type-1 extensions are clarified through a new generalization of d-separation.