Lifted Inference for Relational Continuous Models

TL;DR

This paper introduces a novel exact lifted inference algorithm for Relational Continuous Models that significantly improves efficiency, especially for Gaussian potentials, enabling scalable inference in large, real-world applications.

Contribution

The paper presents the first exact lifted inference algorithm for RCMs, with linear-time complexity for Gaussian potentials, advancing scalable probabilistic reasoning in relational continuous domains.

Findings

Algorithm achieves linear-time inference with Gaussian potentials.

Outperforms existing ground-level and lifted inference methods.

Demonstrated effectiveness on econometrics example.

Abstract

Relational Continuous Models (RCMs) represent joint probability densities over attributes of objects, when the attributes have continuous domains. With relational representations, they can model joint probability distributions over large numbers of variables compactly in a natural way. This paper presents a new exact lifted inference algorithm for RCMs, thus it scales up to large models of real world applications. The algorithm applies to Relational Pairwise Models which are (relational) products of potentials of arity 2. Our algorithm is unique in two ways. First, it substantially improves the efficiency of lifted inference with variables of continuous domains. When a relational model has Gaussian potentials, it takes only linear-time compared to cubic time of previous methods. Second, it is the first exact inference algorithm which handles RCMs in a lifted way. The algorithm is illustrated over an example from econometrics. Experimental results show that our algorithm outperforms both a groundlevel inference algorithm and an algorithm built with previously-known lifted methods.