Inference in higher-order undirected graphical models and binary polynomial optimization

TL;DR

This paper addresses inference in higher-order undirected graphical models with binary labels by formulating it as a binary polynomial optimization problem, proposing LP relaxations, and demonstrating their effectiveness in image restoration and error-correcting code decoding.

Contribution

It introduces new linear programming relaxations for binary polynomial optimization in higher-order graphical models and compares their theoretical strength.

Findings

LP relaxations are effective for image restoration

LP relaxations improve decoding error-correcting codes

Theoretical comparison shows varying strengths of relaxations

Abstract

We consider the problem of inference in higher-order undirected graphical models with binary labels. We formulate this problem as a binary polynomial optimization problem and propose several linear programming relaxations for it. We compare the strength of the proposed linear programming relaxations theoretically. Finally, we demonstrate the effectiveness of these relaxations by performing a computational study for two important applications, namely, image restoration and decoding error-correcting codes.