Probabilistic Argumentation and Information Algebras of Probability Potentials on Families of Compatible Frames

TL;DR

This paper introduces probabilistic argumentation structures on families of compatible frames, generalizing Bayesian networks, and develops an algebraic framework for inference and optimization within this setting.

Contribution

It generalizes multivariate probabilistic models using compatible frames and establishes an algebraic structure enabling inference similar to Bayesian networks.

Findings

Probabilistic argumentation structures generate probability potentials on compatible frames.

An algebraic structure similar to valuation algebras is developed for these potentials.

Inference and optimization techniques like max/prod are applicable within this framework.

Abstract

Probabilistic argumentation is an alternative to causal modeling with Bayesian networks. Probabilistic argumentation structures (PAS) are defined on families of compatible frames (f.c.f). This is a generalization of the usual multivariate models based on families of variables. The crucial relation of conditional independence between frames of a f.c.f is introduced and shown to form a quasi-separoid, a weakening of the well-known structure of a separoid. It is shown that PAS generate probability potentials on the frames of the f.c.f. The operations of aggregating different PAS and of transport of a PAS from one frame to another induce an algebraic structure on the family of potentials on the f.c.f, an algebraic structure which is similar to valuation algebras related to Bayesian networks, but more general. As a consequence the well-known local computation architectures of Bayesian networks for inference apply also for the potentials on f.c.f. Conditioning and conditionals can be defined for potentials and it is shown that these concepts satisfy similar properties as conditional probability distributions. Finally a max/prod algebra between potentials is defined and applied to find most probable configurations for a factorization of potentials.