Convergence rate analysis of MAP coordinate minimization algorithms

Ofer Meshi, Tommi Jaakkola, Amir Globerson

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Finding maximum a posteriori (MAP) assignments in graphical models is an important task in many applications. Since the problem is generally hard, linear programming (LP) relaxations are often used. Solving these relaxations efficiently is thus an important practical problem. In recent years, several authors have proposed message passing updates corresponding to coordinate descent in the dual LP. However, these are generally not guaranteed to converge to a global optimum. One approach to remedy this is to smooth the LP, and perform coordinate descent on the smoothed dual. However, little is known about the convergence rate of this procedure. Here we perform a thorough rate analysis of such schemes and derive primal and dual convergence rates. We also provide a simple dual to primal mapping that yields feasible primal solutions with a guaranteed rate of convergence. Empirical evaluation supports our theoretical claims and shows that the method is highly competitive with state of the art approaches that yield global optima.

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 25
Subtitle of host publication26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012
Pages3014-3022
Number of pages9
StatePublished - 2012
Externally publishedYes
Event26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012 - Lake Tahoe, NV, United States
Duration: 3 Dec 20126 Dec 2012

Publication series

NameAdvances in Neural Information Processing Systems
Volume4
ISSN (Print)1049-5258

Conference

Conference26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012
Country/TerritoryUnited States
CityLake Tahoe, NV
Period3/12/126/12/12

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