DeepAI
Log In Sign Up

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

12/04/2020
by   Chirag Pabbaraju, et al.
0

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.

READ FULL TEXT

page 9

page 23

page 24

06/01/2017

The Mixing method: coordinate descent for low-rank semidefinite programming

In this paper, we propose a coordinate descent approach to low-rank stru...
11/24/2021

Efficient semidefinite bounds for multi-label discrete graphical models

By concisely representing a joint function of many variables as the comb...
05/19/2014

Scalable Semidefinite Relaxation for Maximum A Posterior Estimation

Maximum a posteriori (MAP) inference over discrete Markov random fields ...
05/24/2021

Partition Function Estimation: A Quantitative Study

Probabilistic graphical models have emerged as a powerful modeling tool ...
07/22/2017

Coarse-to-Fine Lifted MAP Inference in Computer Vision

There is a vast body of theoretical research on lifted inference in prob...
04/16/2020

MPLP++: Fast, Parallel Dual Block-Coordinate Ascent for Dense Graphical Models

Dense, discrete Graphical Models with pairwise potentials are a powerful...
10/27/2018

Accelerated Inference in Markov Random Fields via Smooth Riemannian Optimization

Markov Random Fields (MRFs) are a popular model for several pattern reco...