Lifted Relax, Compensate and then Recover: From Approximate to Exact Lifted Probabilistic Inference

TL;DR

This paper introduces a novel lifted inference method that relaxes, compensates, and recovers first-order constraints to efficiently approximate and eventually perform exact inference in probabilistic models like Markov logic networks.

Contribution

It presents a new framework that transitions from approximate to exact lifted inference through iterative relaxation and constraint recovery at the first-order level.

Findings

Significantly improves approximation quality over propositional solvers.

Outperforms lifted belief propagation in empirical evaluations.

Provides a flexible spectrum from approximate to exact inference.

Abstract

We propose an approach to lifted approximate inference for first-order probabilistic models, such as Markov logic networks. It is based on performing exact lifted inference in a simplified first-order model, which is found by relaxing first-order constraints, and then compensating for the relaxation. These simplified models can be incrementally improved by carefully recovering constraints that have been relaxed, also at the first-order level. This leads to a spectrum of approximations, with lifted belief propagation on one end, and exact lifted inference on the other. We discuss how relaxation, compensation, and recovery can be performed, all at the firstorder level, and show empirically that our approach substantially improves on the approximations of both propositional solvers and lifted belief propagation.