Exact Inference for Relational Graphical Models with Interpreted Functions: Lifted Probabilistic Inference Modulo Theories

TL;DR

This paper introduces a lifted exact inference algorithm for relational graphical models that efficiently handles random functions, relations, and complex theories involving arithmetic and inequalities.

Contribution

It extends Probabilistic Inference Modulo Theories by incorporating random functions and relations, enabling more expressive and efficient inference.

Findings

First exact inference algorithm for models with functions and relations

Efficiently exploits theories with arithmetic and inequalities

Advances lifted probabilistic inference capabilities

Abstract

Probabilistic Inference Modulo Theories (PIMT) is a recent framework that expands exact inference on graphical models to use richer languages that include arithmetic, equalities, and inequalities on both integers and real numbers. In this paper, we expand PIMT to a lifted version that also processes random functions and relations. This enhancement is achieved by adapting Inversion, a method from Lifted First-Order Probabilistic Inference literature, to also be modulo theories. This results in the first algorithm for exact probabilistic inference that efficiently and simultaneously exploits random relations and functions, arithmetic, equalities and inequalities.