An Efficient Message-Passing Algorithm for the M-Best MAP Problem

Dhruv Batra
Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, PMLR R10:119-128, 2012.

Abstract

Much effort has been directed at algorithms for obtaining the highest probability configuration in a probabilistic random field model known as the maximum a posteriori (MAP) inference problem. In many situations, one could benefit from having not just a single solution, but the top M most probable solutions known as the M-Best MAP problem. In this paper, we propose an efficient message-passing based algorithm for solving the M-Best MAP problem. Specifically, our algorithm solves the recently proposed Linear Programming (LP) formulation of M-Best MAP [7], while being orders of magnitude faster than a generic LP-solver. Our approach relies on studying a particular partial Lagrangian relaxation of the M-Best MAP LP which exposes a natural combinatorial structure of the problem that we exploit.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR10-batra12a, title = {An Efficient Message-Passing Algorithm for the M-Best {MAP} Problem}, author = {Batra, Dhruv}, booktitle = {Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence}, pages = {119--128}, year = {2012}, editor = {de Freitas, Nando and Murphy, Kevin}, volume = {R10}, series = {Proceedings of Machine Learning Research}, month = {14--18 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r10/main/assets/batra12a/batra12a.pdf}, url = {https://proceedings.mlr.press/r10/batra12a.html}, abstract = {Much effort has been directed at algorithms for obtaining the highest probability configuration in a probabilistic random field model known as the maximum a posteriori (MAP) inference problem. In many situations, one could benefit from having not just a single solution, but the top M most probable solutions known as the M-Best MAP problem. In this paper, we propose an efficient message-passing based algorithm for solving the M-Best MAP problem. Specifically, our algorithm solves the recently proposed Linear Programming (LP) formulation of M-Best MAP [7], while being orders of magnitude faster than a generic LP-solver. Our approach relies on studying a particular partial Lagrangian relaxation of the M-Best MAP LP which exposes a natural combinatorial structure of the problem that we exploit.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T An Efficient Message-Passing Algorithm for the M-Best MAP Problem %A Dhruv Batra %B Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2012 %E Nando de Freitas %E Kevin Murphy %F pmlr-vR10-batra12a %I PMLR %P 119--128 %U https://proceedings.mlr.press/r10/batra12a.html %V R10 %X Much effort has been directed at algorithms for obtaining the highest probability configuration in a probabilistic random field model known as the maximum a posteriori (MAP) inference problem. In many situations, one could benefit from having not just a single solution, but the top M most probable solutions known as the M-Best MAP problem. In this paper, we propose an efficient message-passing based algorithm for solving the M-Best MAP problem. Specifically, our algorithm solves the recently proposed Linear Programming (LP) formulation of M-Best MAP [7], while being orders of magnitude faster than a generic LP-solver. Our approach relies on studying a particular partial Lagrangian relaxation of the M-Best MAP LP which exposes a natural combinatorial structure of the problem that we exploit. %Z Reissued by PMLR on 04 October 2026.
APA
Batra, D.. (2012). An Efficient Message-Passing Algorithm for the M-Best MAP Problem. Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R10:119-128 Available from https://proceedings.mlr.press/r10/batra12a.html. Reissued by PMLR on 04 October 2026.

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