Exploiting Causal Independence in Markov Logic Networks: Combining Undirected and Directed Models

A new method is proposed for compiling causal independencies into Markov logic networks. A Markov logic network can be viewed as compactly representing a factorization of a joint probability into the multiplication of a set of factors guided by logical formulas. We present a notion of causal independence that enables one to further factorize the factors into a combination of even smaller factors and consequently obtain a finer-grain factorization of the joint probability. The causal independence lets us specify the factor in terms of weighted, directed clauses and an associative and commutative operator, such as "or", "sum" or "max", on the contribution of the variables involved in the factors, hence combining both undirected and directed knowledge.