Exact Inference in High-order Structured Prediction

TL;DR

This paper introduces a two-stage convex optimization method for exact inference in high-order structured prediction tasks, leveraging hypergraph properties and a Cheeger-type inequality to improve label recovery in Markov random fields.

Contribution

The paper proposes a novel two-stage convex optimization algorithm for exact high-order inference and introduces hypergraph expansion properties that influence inference success.

Findings

The algorithm achieves exact label recovery in high-order Markov random fields.

Hyperedge expansion properties are key to inference success.

A new hypergraph Cheeger-type inequality links hypergraph structure to inference performance.

Abstract

In this paper, we study the problem of inference in high-order structured prediction tasks. In the context of Markov random fields, the goal of a high-order inference task is to maximize a score function on the space of labels, and the score function can be decomposed into sum of unary and high-order potentials. We apply a generative model approach to study the problem of high-order inference, and provide a two-stage convex optimization algorithm for exact label recovery. We also provide a new class of hypergraph structural properties related to hyperedge expansion that drives the success in general high-order inference problems. Finally, we connect the performance of our algorithm and the hyperedge expansion property using a novel hypergraph Cheeger-type inequality.