Learning Directed Relational Models with Recursive Dependencies

Abstract

Abstract. Recently, there has been an increasing interest in generative relational models that represent probabilistic patterns over both links and attributes. A key characteristic of relational data is that the value of a predicate often depends on values of the same predicate for related entities. In this paper we present a new approach to learning directed relational models which utilizes two key concepts: a pseudo likelihood measure that is well defined for recursive dependencies, and the notion of stratification from logic programming. An issue for modelling recursive dependencies with Bayes nets are redundant edges that increase the complexity of learning. We propose a new normal form for 1st-order Bayes nets that removes the redundancy, and prove that assuming stratification, the normal form constraints involve no loss of modelling power. We incorporate these constraints in the learn-and-join algorithm of Khosravi et al., which is a stateof-the art structure learning algorithm that upgrades propositional Bayes net learners for relational data. Emprical evaluation compares our approach to learning recursive dependencies with undirected models (Markov Logic Networks). The Bayes net approach is orders of magnitude faster, and learns more recursive dependencies, which lead to more accurate predictions.

Learning graphical models for relational data via lattice search

“…This indicates that the discovered recursive dependencies are important for improving predictions. For further discussion, please see Schulte et al (2011). Table 12 Autocorrelations discovered by the learn-and-join algorithm using the main functor constraints…”

“…We have also added more comparison with other Markov Logic Network learning methods (e.g., BUSL, LSM) and a lesion study that assesses the effects of using only part of the components of our main algorithm. Our approach to autocorrelations (recursive dependencies) was presented by Schulte et al (2011). The main idea is to use a restricted form of Bayes net that we call the main functor node format.…”

“…Following Schulte et al (2011), the algorithm requires the specification of a main functor node for each functor (e.g., Smokes(Y ) is the main functor node for the functor Smokes).…”