In many probabilistic first-order representation systems, inference is performed by "grounding"---i.e., mapping it to a propositional representation, and then performing propositional inference. With a large database of facts, groundings can be very large, making inference and learning computationally expensive. Here we present a first-order probabilistic language which is well-suited to approximate "local" grounding: every query @math can be approximately grounded with a small graph. The language is an extension of stochastic logic programs where inference is performed by a variant of personalized PageRank. Experimentally, we show that the approach performs well without weight learning on an entity resolution task; that supervised weight-learning improves accuracy; and that grounding time is independent of DB size. We also show that order-of-magnitude speedups are possible by parallelizing learning.
Although we have chosen here to compare experimentally to MLNs @cite_6 @cite_18 , ProPPR represents a rather different philosophy toward language design: rather than beginning with a highly-expressive but intractible logical core, we begin with a limited logical inference scheme and add to it a minimal set of extensions that allow probabilistic reasoning, while maintaining stable, efficient inference and learning. While ProPPR is less expressive than MLNs (for instance, it is limited to definite clause theories) it is also much more efficient. This philosophy is similar to that illustrated by probabilistic similarity logic (PSL) @cite_3 ; however, unlike ProPPR, PSL does not include a local'' grounding procedure, which leads to small inference problems, even for large databases.
@cite_18 @cite_3 @cite_6
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Entity resolution is the problem of determining which records in a database refer to the same entities, and is a crucial and expensive step in the data mining process. Interest in it has grown rapidly in recent years, and many approaches have been proposed. However, they tend to address only isolated aspects of the problem, and are often ad hoc. This paper proposes a well-founded, integrated solution to the entity resolution problem based on Markov logic. Markov logic combines first-order logic and probabilistic graphical models by attaching weights to first-order formulas, and viewing them as templates for features of Markov networks. We show how a number of previous approaches can be formulated and seamlessly combined in Markov logic, and how the resulting learning and inference problems can be solved efficiently. Experiments on two citation databases show the utility of this approach, and evaluate the contribution of the different components. We propose a simple approach to combining first-order logic and probabilistic graphical models in a single representation. A Markov logic network (MLN) is a first-order knowledge base with a weight attached to each formula (or clause). Together with a set of constants representing objects in the domain, it specifies a ground Markov network containing one feature for each possible grounding of a first-order formula in the KB, with the corresponding weight. Inference in MLNs is performed by MCMC over the minimal subset of the ground network required for answering the query. Weights are efficiently learned from relational databases by iteratively optimizing a pseudo-likelihood measure. Optionally, additional clauses are learned using inductive logic programming techniques. Experiments with a real-world database and knowledge base in a university domain illustrate the promise of this approach.