Equitable Partitions of Concave Free Energies

Martin Mladenov, Kristian Kersting
Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence, PMLR R13:692-701, 2015.

Abstract

Recently, exploiting symmetries within variational inference has been algebraically formalized. With the exception of TRW for marginal inference, however, the framework resulted in approximate MAP algorithms only, based on equitable and orbit partitions of the graphical model. Here, we deepen our understandnig of it for marginal inference. Specifically, we show that a large class of concave free energies admits equitable partitions, of which orbit partitions are a special case, that can be exploited for lifting. Although already interesting on its own, we go one step further. We demonstrate that concave free energies can be reparameterized so that existing convergent algorithms can be used for lifted variational marginal inference without modification.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR13-mladenov15a, title = {Equitable Partitions of Concave Free Energies}, author = {Mladenov, Martin and Kersting, Kristian}, booktitle = {Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence}, pages = {692--701}, year = {2015}, editor = {Meila, Marina and Heskes, Tom}, volume = {R13}, series = {Proceedings of Machine Learning Research}, month = {12--16 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r13/main/assets/mladenov15a/mladenov15a.pdf}, url = {https://proceedings.mlr.press/r13/mladenov15a.html}, abstract = {Recently, exploiting symmetries within variational inference has been algebraically formalized. With the exception of TRW for marginal inference, however, the framework resulted in approximate MAP algorithms only, based on equitable and orbit partitions of the graphical model. Here, we deepen our understandnig of it for marginal inference. Specifically, we show that a large class of concave free energies admits equitable partitions, of which orbit partitions are a special case, that can be exploited for lifting. Although already interesting on its own, we go one step further. We demonstrate that concave free energies can be reparameterized so that existing convergent algorithms can be used for lifted variational marginal inference without modification.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Equitable Partitions of Concave Free Energies %A Martin Mladenov %A Kristian Kersting %B Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2015 %E Marina Meila %E Tom Heskes %F pmlr-vR13-mladenov15a %I PMLR %P 692--701 %U https://proceedings.mlr.press/r13/mladenov15a.html %V R13 %X Recently, exploiting symmetries within variational inference has been algebraically formalized. With the exception of TRW for marginal inference, however, the framework resulted in approximate MAP algorithms only, based on equitable and orbit partitions of the graphical model. Here, we deepen our understandnig of it for marginal inference. Specifically, we show that a large class of concave free energies admits equitable partitions, of which orbit partitions are a special case, that can be exploited for lifting. Although already interesting on its own, we go one step further. We demonstrate that concave free energies can be reparameterized so that existing convergent algorithms can be used for lifted variational marginal inference without modification. %Z Reissued by PMLR on 04 October 2026.
APA
Mladenov, M. & Kersting, K.. (2015). Equitable Partitions of Concave Free Energies. Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R13:692-701 Available from https://proceedings.mlr.press/r13/mladenov15a.html. Reissued by PMLR on 04 October 2026.

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