Efficient semidefinite-programming-based inference for binary and multi-class MRFs

TL;DR

This paper introduces an efficient semidefinite programming approach for probabilistic inference in binary and multi-class Markov Random Fields, significantly improving speed and solution quality over existing methods, and scaling to large models.

Contribution

It extends semidefinite relaxations to multi-class MRFs and employs a fast coordinate-descent SDP solver for practical, scalable inference.

Findings

Outperforms existing methods in solution quality and speed

Successfully scales to large, fully-connected MRFs in computer vision

Provides a practical approach for complex probabilistic inference

Abstract

Probabilistic inference in pairwise Markov Random Fields (MRFs), i.e. computing the partition function or computing a MAP estimate of the variables, is a foundational problem in probabilistic graphical models. Semidefinite programming relaxations have long been a theoretically powerful tool for analyzing properties of probabilistic inference, but have not been practical owing to the high computational cost of typical solvers for solving the resulting SDPs. In this paper, we propose an efficient method for computing the partition function or MAP estimate in a pairwise MRF by instead exploiting a recently proposed coordinate-descent-based fast semidefinite solver. We also extend semidefinite relaxations from the typical binary MRF to the full multi-class setting, and develop a compact semidefinite relaxation that can again be solved efficiently using the solver. We show that the method substantially outperforms (both in terms of solution quality and speed) the existing state of the art in approximate inference, on benchmark problems drawn from previous work. We also show that our approach can scale to large MRF domains such as fully-connected pairwise CRF models used in computer vision.