Lifted Probabilistic Inference for Asymmetric Graphical Models

TL;DR

This paper introduces a sampling-based inference framework that leverages approximate symmetries in asymmetric graphical models, improving probability estimates without bias and outperforming existing MCMC methods.

Contribution

It presents a novel framework for probabilistic inference that uses approximate symmetries directly, avoiding the need for model symmetry and reducing bias in probability estimation.

Findings

Outperforms existing MCMC algorithms in experiments

Provides unbiased probability estimates using approximate symmetries

Works directly on asymmetric models without requiring symmetry induction

Abstract

Lifted probabilistic inference algorithms have been successfully applied to a large number of symmetric graphical models. Unfortunately, the majority of real-world graphical models is asymmetric. This is even the case for relational representations when evidence is given. Therefore, more recent work in the community moved to making the models symmetric and then applying existing lifted inference algorithms. However, this approach has two shortcomings. First, all existing over-symmetric approximations require a relational representation such as Markov logic networks. Second, the induced symmetries often change the distribution significantly, making the computed probabilities highly biased. We present a framework for probabilistic sampling-based inference that only uses the induced approximate symmetries to propose steps in a Metropolis-Hastings style Markov chain. The framework, therefore, leads to improved probability estimates while remaining unbiased. Experiments demonstrate that the approach outperforms existing MCMC algorithms.