Lifted inference for relational continuous models

Relational Continuous Models (RCMs) represent joint prob-ability densities over attributes of objects, when the attributes have continuous domains. With relational representation, they can model joint probability distributions over large num-bers 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 ap-plications. The algorithm applies to relational pairwise mod-els 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 ex-ample from Econometrics. Experimental results show that our algorithm outperforms both a ground-level inference al-gorithm and an algorithm built with previously-known lifted methods.