Lifted Message Passing for the Generalized Belief Propagation

TL;DR

This paper presents a lifted GBP message passing algorithm that efficiently computes sum-product queries in Probabilistic Relational Models by exploiting cluster symmetries, reducing complexity and domain dependence.

Contribution

The paper introduces a novel lifted GBP algorithm that uses graph isomorphism tests to form compact region graphs, enabling scalable inference in complex probabilistic models.

Findings

Reduces complexity of GBP in relational models.

Handles complex models with domain-size independence.

Maintains GBP behavior in lifted form.

Abstract

We introduce the lifted Generalized Belief Propagation (GBP) message passing algorithm, for the computation of sum-product queries in Probabilistic Relational Models (e.g. Markov logic network). The algorithm forms a compact region graph and establishes a modified version of message passing, which mimics the GBP behavior in a corresponding ground model. The compact graph is obtained by exploiting a graphical representation of clusters, which reduces cluster symmetry detection to isomorphism tests on small local graphs. The framework is thus capable of handling complex models, while remaining domain-size independent.