Lifted Inference for Relational Continuous Models
  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.
