Computing marginal distributions over continuous markov networks for statistical relational learning

Continuous Markov random fields are a general formalism to model joint proba-bility distributions over events with continuous outcomes. We prove that marginal
computation for constrained continuous MRFs is #P-hard in general and present
a polynomial-time approximation scheme under mild assumptions on the struc-
ture of the random field. Moreover, we introduce a sampling algorithm to com-
pute marginal distributions and develop novel techniques to increase its effi-
ciency. Continuous MRFs are a general purpose probabilistic modeling tool and
we demonstrate how they can be applied to statistical relational learning. On the
problem of collective classification, we evaluate our algorithm and show that the
standard deviation of marginals serves as a useful measure of confidence.