Efficiently Searching for Frustrated Cycles in MAP Inference

TL;DR

This paper introduces a nearly linear time algorithm for finding the most frustrated cycle in graphical models, improving MAP inference by integrating cycle constraints efficiently.

Contribution

It presents a novel nearly linear time algorithm for searching arbitrary length frustrated cycles and integrates it into dual decomposition for MAP inference.

Findings

Exact solutions for MAP inference in relational classification

Effective cycle constraint enforcement in stereo vision

Improved inference accuracy with cycle-based constraints

Abstract

Dual decomposition provides a tractable framework for designing algorithms for finding the most probable (MAP) configuration in graphical models. However, for many real-world inference problems, the typical decomposition has a large integrality gap, due to frustrated cycles. One way to tighten the relaxation is to introduce additional constraints that explicitly enforce cycle consistency. Earlier work showed that cluster-pursuit algorithms, which iteratively introduce cycle and other higherorder consistency constraints, allows one to exactly solve many hard inference problems. However, these algorithms explicitly enumerate a candidate set of clusters, limiting them to triplets or other short cycles. We solve the search problem for cycle constraints, giving a nearly linear time algorithm for finding the most frustrated cycle of arbitrary length. We show how to use this search algorithm together with the dual decomposition framework and clusterpursuit. The new algorithm exactly solves MAP inference problems arising from relational classification and stereo vision.