Lifted Inference for Relational Continuous Models

Abstract

Relational Continuous Models (RCMs) represent joint probability densities over attributes of objects, when the attributes have continuous domains. With relational representation, they can model joint probability distributions over large numbers of variables compactly in a natural way. This paper presents the first exact inference algorithm for RCMs at a lifted level, 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 is an efficient lifted inference algorithm. When Gaussian potentials are used, it takes only linear time while existing methods take cubic time. 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 ground-level inference algorithm and an algorithm built with previously-known lifted methods.