Soft evidential update for probabilistic multiagent systems

Abstract

We address the problem of updating a probability distribution represented by a Bayesian network upon presentation of soft evidence. Our motivation is the desire to let agents communicate with each other by exchanging beliefs, as in the Agent-Encapsulated Bayesian Network (AEBN) model, and soft evidential update (under several different names) is a problem with a long history. We give methodological guidance to model soft evidence in the form of beliefs (marginals) on single and multiple variables, propositional logical formulae (arbitrary events in the universe of discourse), and even conditional distributions, by introducing observation variables and explaining their use. The extended networks with observation variables fully capture the independence structure of the model, even upon receipt of soft evidence. We provide two algorithms that extend the celebrated junction tree algorithm, process soft evidence, and have different efficiency characteristics. One of the extensions, the big clique algorithm, promises to be more time efficient at the cost of possible space penalties. The other extension requires only minimal modifications to the junction tree at the cost of possibly substantial time penalties. Our results open new avenues of application for graphical probabilistic models.