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Relational Continuous Models (RCMs) represent joint probability densitiesover attributes of objects, when the attributes have continuous domains. Withrelational representations, they can model joint probability distributions overlarge numbers of variables compactly in a natural way. This paper presents anew exact lifted inference algorithm for RCMs, thus it scales up to largemodels of real world applications. The algorithm applies to Relational PairwiseModels which are (relational) products of potentials of arity 2. Our algorithmis unique in two ways. First, it substantially improves the efficiency oflifted inference with variables of continuous domains. When a relational modelhas Gaussian potentials, it takes only linear-time compared to cubic time ofprevious methods. Second, it is the first exact inference algorithm whichhandles RCMs in a lifted way. The algorithm is illustrated over an example fromeconometrics. Experimental results show that our algorithm outperforms both agroundlevel inference algorithm and an algorithm built with previously-knownlifted methods.

Lifted Inference for Relational Continuous Models