Convergent and Correct Message Passing Schemes for Optimization Problems over Graphical Models

Nicholas Ruozzi, Sekhar Tatikonda
Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, PMLR R8:499-499, 2010.

Abstract

The max-product algorithm, which attempts to compute the most probable assignment (MAP) of a given probability distribution, has recently found applications in quadratic minimization and combinatorial optimization. Unfortunately, the max-product algorithm is not guaranteed to converge and, even if it does, is not guaranteed to produce the MAP assignment. In this work, we provide a simple derivation of a new family of message passing algorithms by “splitting” the factors of our graphical model. We prove that, for any objective function that attains its maximum value over its domain, this new family of message passing algorithms always contains a message passing scheme that guarantees correctness upon convergence to a unique estimate. Finally, we adopt an asynchronous message passing schedule and prove that, under mild assumptions, such a schedule guarantees the convergence of our algorithm.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR8-ruozzi10a, title = {Convergent and Correct Message Passing Schemes for Optimization Problems over Graphical Models}, author = {Ruozzi, Nicholas and Tatikonda, Sekhar}, booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence}, pages = {499--499}, year = {2010}, editor = {Grünwald, Peter and Spirtes, Peter}, volume = {R8}, series = {Proceedings of Machine Learning Research}, month = {08--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r8/main/assets/ruozzi10a/ruozzi10a.pdf}, url = {https://proceedings.mlr.press/r8/ruozzi10a.html}, abstract = {The max-product algorithm, which attempts to compute the most probable assignment (MAP) of a given probability distribution, has recently found applications in quadratic minimization and combinatorial optimization. Unfortunately, the max-product algorithm is not guaranteed to converge and, even if it does, is not guaranteed to produce the MAP assignment. In this work, we provide a simple derivation of a new family of message passing algorithms by “splitting” the factors of our graphical model. We prove that, for any objective function that attains its maximum value over its domain, this new family of message passing algorithms always contains a message passing scheme that guarantees correctness upon convergence to a unique estimate. Finally, we adopt an asynchronous message passing schedule and prove that, under mild assumptions, such a schedule guarantees the convergence of our algorithm.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Convergent and Correct Message Passing Schemes for Optimization Problems over Graphical Models %A Nicholas Ruozzi %A Sekhar Tatikonda %B Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2010 %E Peter Grünwald %E Peter Spirtes %F pmlr-vR8-ruozzi10a %I PMLR %P 499--499 %U https://proceedings.mlr.press/r8/ruozzi10a.html %V R8 %X The max-product algorithm, which attempts to compute the most probable assignment (MAP) of a given probability distribution, has recently found applications in quadratic minimization and combinatorial optimization. Unfortunately, the max-product algorithm is not guaranteed to converge and, even if it does, is not guaranteed to produce the MAP assignment. In this work, we provide a simple derivation of a new family of message passing algorithms by “splitting” the factors of our graphical model. We prove that, for any objective function that attains its maximum value over its domain, this new family of message passing algorithms always contains a message passing scheme that guarantees correctness upon convergence to a unique estimate. Finally, we adopt an asynchronous message passing schedule and prove that, under mild assumptions, such a schedule guarantees the convergence of our algorithm. %Z Reissued by PMLR on 04 October 2026.
APA
Ruozzi, N. & Tatikonda, S.. (2010). Convergent and Correct Message Passing Schemes for Optimization Problems over Graphical Models. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R8:499-499 Available from https://proceedings.mlr.press/r8/ruozzi10a.html. Reissued by PMLR on 04 October 2026.

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