Improving Learning of Markov Logic Networks using Transfer and Bottom-Up Induction (2007)
Statistical relational learning (SRL) algorithms combine ideas from rich knowledge representations, such as first-order logic, with those from probabilistic graphical models, such as Markov networks, to address the problem of learning from multi-relational data. One challenge posed by such data is that individual instances are frequently very large and include complex relationships among the entities. Moreover, because separate instances do not follow the same structure and contain varying numbers of entities, they cannot be effectively represented as a feature-vector. SRL models and algorithms have been successfully applied to a wide variety of domains such as social network analysis, biological data analysis, and planning, among others. Markov logic networks (MLNs) are a recently-developed SRL model that consists of weighted first-order clauses. MLNs can be viewed as templates that define Markov networks when provided with the set of constants present in a domain. MLNs are therefore very powerful because they inherit the expressivity of first-order logic. At the same time, MLNs can flexibly deal with noisy or uncertain data to produce probabilistic predictions for a set of propositions. MLNs have also been shown to subsume several other popular SRL models.

The expressive power of MLNs comes at a cost: structure learning, or learning the first-order clauses of the model, is a very computationally intensive process that needs to sift through a large hypothesis space with many local maxima and plateaus. It is therefore an important research problem to develop learning algorithms that improve the speed and accuracy of this process. The main contribution of this proposal are two algorithms for learning the structure of MLNs that proceed in a more data-driven fashion, in contrast to most existing SRL algorithms. The first algorithm we present, R-TAMAR, improves learning by transferring the structure of an MLN learned in a domain related to the current one. It first diagnoses the transferred structure and then focuses its efforts only on the regions it determines to be incorrect. Our second algorithm, BUSL improves structure learning from scratch by approaching the problem in a more bottom-up fashion and first constructing a variablized Markov network template that significantly constrains the space of viable clause candidates. We demonstrate the effectiveness of our methods in three social domains.

Our proposed future work directions include testing BUSL in additional domains and extending it so that it can be used not only to learn from scratch, but also to revise a provided MLN structure. Our most ambitious long-term goal is to develop a system that transfers knowledge from multiple potential sources. An important prerequisite to such a system is a method for measuring the similarity between domains. We would also like to extend BUSL to learn other SRL models and to handle functions.

Technical Report UT-AI-TR-07-341, Artificial Intelligence Lab, University of Texas at Austin.

Lilyana Mihalkova Ph.D. Alumni lilymihal [at] gmail com