Gauged Mini-Bucket Elimination for Approximate Inference
Sungsoo Ahn, Michael Chertkov, Jinwoo Shin, Adrian Weller
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.
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.}
}