Efficient Localized Inference for Large Graphical Models

TL;DR

This paper introduces a localized inference algorithm for large graphical models that efficiently approximates marginal distributions by focusing on a small local region, leveraging correlation decay properties.

Contribution

The paper presents a novel localized inference method with theoretical error bounds and a greedy expansion algorithm for large graphical models.

Findings

The algorithm provides fast, accurate marginal approximations.

Theoretical bounds are validated on various datasets.

Localized inference reduces computational complexity.

Abstract

We propose a new localized inference algorithm for answering marginalization queries in large graphical models with the correlation decay property. Given a query variable and a large graphical model, we define a much smaller model in a local region around the query variable in the target model so that the marginal distribution of the query variable can be accurately approximated. We introduce two approximation error bounds based on the Dobrushin's comparison theorem and apply our bounds to derive a greedy expansion algorithm that efficiently guides the selection of neighbor nodes for localized inference. We verify our theoretical bounds on various datasets and demonstrate that our localized inference algorithm can provide fast and accurate approximation for large graphical models.