Recursive Random Fields

Daniel Lowd and Pedro Domingos


A formula in first-order logic can be viewed as a tree, with a logical connective at each node, and a knowledge base can be viewed as a tree whose root is a conjunction. Markov logic [Richardson and Domingos, 2006] makes this conjunction probabilistic, as well as the universal quantifiers directly under it, but the rest of the tree remains purely logical. This causes an asymmetry in the treatment of conjunctions and disjunctions, and of universal and existential quantifiers. We propose to overcome this by allowing the features of Markov logic networks (MLNs) to be nested MLNs. We call this representation recursive random fields (RRFs). RRFs can represent many first-order distributions exponentially more compactly than MLNs. We perform inference in RRFs using MCMC and ICM, and weight learning using a form of backpropagation. Weight learning in RRFs is more powerful than structure learning in MLNs. Applied to first-order knowledge bases, it provides a very flexible form of theory revision. We evaluate RRFs on the problem of probabilistic integrity constraints in databases, and obtain promising results.