Extended Lifted Inference with Joint Formulas

TL;DR

This paper extends the First-Order Variable Elimination algorithm with new conversion operators, enabling more efficient exact inference and decision-making in relational probabilistic models.

Contribution

Introduction of joint formula conversion and just-different counting conversion operators to expand FOVE's applicability and efficiency.

Findings

Significant speedup over existing methods.

Extended inference capabilities on relational models.

Exact solutions for MEU queries in decision models.

Abstract

The First-Order Variable Elimination (FOVE) algorithm allows exact inference to be applied directly to probabilistic relational models, and has proven to be vastly superior to the application of standard inference methods on a grounded propositional model. Still, FOVE operators can be applied under restricted conditions, often forcing one to resort to propositional inference. This paper aims to extend the applicability of FOVE by providing two new model conversion operators: the first and the primary is joint formula conversion and the second is just-different counting conversion. These new operations allow efficient inference methods to be applied directly on relational models, where no existing efficient method could be applied hitherto. In addition, aided by these capabilities, we show how to adapt FOVE to provide exact solutions to Maximum Expected Utility (MEU) queries over relational models for decision under uncertainty. Experimental evaluations show our algorithms to provide significant speedup over the alternatives.