Template Based Inference in Symmetric Relational Markov Random Fields

TL;DR

This paper introduces a template-based belief propagation method for symmetric relational Markov Random Fields, significantly speeding up inference and learning in large-scale relational models, demonstrated on protein interaction networks.

Contribution

It presents a novel template-level inference approach for symmetric relational MRFs, reducing computational complexity from domain size to model size, and proves its equivalence to loopy belief propagation.

Findings

Template-based inference speeds up learning in large relational models.

Method is equivalent to synchronous loopy belief propagation.

Successfully applied to protein-protein interaction networks.

Abstract

Relational Markov Random Fields are a general and flexible framework for reasoning about the joint distribution over attributes of a large number of interacting entities. The main computational difficulty in learning such models is inference. Even when dealing with complete data, where one can summarize a large domain by sufficient statistics, learning requires one to compute the expectation of the sufficient statistics given different parameter choices. The typical solution to this problem is to resort to approximate inference procedures, such as loopy belief propagation. Although these procedures are quite efficient, they still require computation that is on the order of the number of interactions (or features) in the model. When learning a large relational model over a complex domain, even such approximations require unrealistic running time. In this paper we show that for a particular class of relational MRFs, which have inherent symmetry, we can perform the inference needed for learning procedures using a template-level belief propagation. This procedure's running time is proportional to the size of the relational model rather than the size of the domain. Moreover, we show that this computational procedure is equivalent to sychronous loopy belief propagation. This enables a dramatic speedup in inference and learning time. We use this procedure to learn relational MRFs for capturing the joint distribution of large protein-protein interaction networks.