Revising Markov boundary for multiagent probabilistic inference

Abstract

Multiply sectioned Bayesian networks (MSBNs) extend Bayesian networks (BNs) to graphical models that provide a coherent framework for probabilistic inference in cooperative multiagent distributed interpretation systems. Observation plays an important role in the inference with graphical models. Since observation of each observable variable has a cost, it would be helpful if we can find the most relevant variables to observe. In a probabilistic model, a Markov boundary of a variable provides a minimal set of variables that shields the variable from the influence of all other variables. However, the concept cannot be used directly for observation. First, it is generally intractable to verify conditional independencies in a probabilistic model. Second, the Markov boundary members may not be observable. Third, it is defined only for a single variable. Finally, it is not unique. By revising the concept to address these issues, we introduce the concept of observable Markov boundary of a set of nodes defined on d-separation of graphical models. The observable Markov boundary captures all relevant variables to observe for probabilistic inference with graphical models. In an MSBN, the observable Markov boundary of a set of nodes may span across all Bayesian subnets. We present an algorithm for cooperative computation of the observable Markov boundary of a set of nodes in an MSBN without revealing subnet structures.