Learning graphical models for relational data via lattice search

Many machine learning applications that involve relational databases incorporate first-order logic and probability. Relational extensions of graphical models include Parametrized Bayes Net (Poole in IJCAI, pp. 985-991, 2003), Probabilistic RelationalModels (Getoor et al. in Introduction to statistical relational learning, pp. 129-173, 2007), and Markov Logic Networks (MLNs) (Domingos and Richardson in Introduction to statistical relational learning, 2007). Many of the current state-of-the-art algorithms for learning MLNs have focused on relatively small datasets with few descriptive attributes, where predicates are mostly binary and the main task is usually prediction of links between entities. This paper addresses what is in a sense a complementary problem: learning the structure of a graphical model that models the distribution of discrete descriptive attributes given the links between entities in a relational database. Descriptive attributes are usually nonbinary and can be very informative, but they increase the search space of possible candidate clauses. We present an efficient new algorithm for learning a Parametrized Bayes Net that performs a level-wise search through the table join lattice for relational dependencies. From the Bayes net we obtain an MLN structure via a standard moralization procedure for converting directed models to undirected models. Learning MLN structure by moralization is 200-1000 times faster and scores substantially higher in predictive accuracy than benchmark MLN algorithms on five relational databases