Gauged Mini-Bucket Elimination for Approximate Inference

Sungsoo Ahn, Michael Chertkov, Jinwoo Shin, Adrian Weller
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:10-19, 2018.

Abstract

Computing the partition function Z of a discrete graphical model is a fundamental inference challenge. Since this is computationally intractable, variational approximations are often used in practice. Recently, so-called gauge transformations were used to improve variational lower bounds on Z. In this paper, we propose a new gauge-variational approach, termed WMBE-G, which combines gauge transformations with the weighted mini-bucket elimination (WMBE) method. WMBE-G can provide both upper and lower bounds on Z, and is easier to optimize than the prior gauge-variational algorithm. We show that WMBE-G strictly improves the earlier WMBE approximation for symmetric models including Ising models with no magnetic field. Our experimental results demonstrate the effectiveness of WMBE-G even for generic, nonsymmetric models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v84-ahn18a, title = {Gauged Mini-Bucket Elimination for Approximate Inference}, author = {Ahn, Sungsoo and Chertkov, Michael and Shin, Jinwoo and Weller, Adrian}, booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics}, pages = {10--19}, year = {2018}, editor = {Storkey, Amos and Perez-Cruz, Fernando}, volume = {84}, series = {Proceedings of Machine Learning Research}, month = {09--11 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v84/ahn18a/ahn18a.pdf}, url = {https://proceedings.mlr.press/v84/ahn18a.html}, abstract = {Computing the partition function Z of a discrete graphical model is a fundamental inference challenge. Since this is computationally intractable, variational approximations are often used in practice. Recently, so-called gauge transformations were used to improve variational lower bounds on Z. In this paper, we propose a new gauge-variational approach, termed WMBE-G, which combines gauge transformations with the weighted mini-bucket elimination (WMBE) method. WMBE-G can provide both upper and lower bounds on Z, and is easier to optimize than the prior gauge-variational algorithm. We show that WMBE-G strictly improves the earlier WMBE approximation for symmetric models including Ising models with no magnetic field. Our experimental results demonstrate the effectiveness of WMBE-G even for generic, nonsymmetric models.} }
Endnote
%0 Conference Paper %T Gauged Mini-Bucket Elimination for Approximate Inference %A Sungsoo Ahn %A Michael Chertkov %A Jinwoo Shin %A Adrian Weller %B Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2018 %E Amos Storkey %E Fernando Perez-Cruz %F pmlr-v84-ahn18a %I PMLR %P 10--19 %U https://proceedings.mlr.press/v84/ahn18a.html %V 84 %X Computing the partition function Z of a discrete graphical model is a fundamental inference challenge. Since this is computationally intractable, variational approximations are often used in practice. Recently, so-called gauge transformations were used to improve variational lower bounds on Z. In this paper, we propose a new gauge-variational approach, termed WMBE-G, which combines gauge transformations with the weighted mini-bucket elimination (WMBE) method. WMBE-G can provide both upper and lower bounds on Z, and is easier to optimize than the prior gauge-variational algorithm. We show that WMBE-G strictly improves the earlier WMBE approximation for symmetric models including Ising models with no magnetic field. Our experimental results demonstrate the effectiveness of WMBE-G even for generic, nonsymmetric models.
APA
Ahn, S., Chertkov, M., Shin, J. & Weller, A.. (2018). Gauged Mini-Bucket Elimination for Approximate Inference. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 84:10-19 Available from https://proceedings.mlr.press/v84/ahn18a.html.

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