The DLR Hierarchy of Approximate Inference
Abstract
We propose a hierarchy for approximate inference based on the Dobrushin, Lanford, Ruelle (DLR) equations. This hierarchy includes existing algorithms, such as belief propagation, and also motivates novel algorithms such as factorized neighbors (FN) algorithms and variants of mean field (MF) algorithms. In particular, we show that extrema of the Bethe free energy correspond to approximate solutions of the DLR equations. In addition, we demonstrate a close connection between these approximate algorithms and Gibbs sampling. Finally, we compare and contrast various of the algorithms in the DLR hierarchy on spin-glass problems. The experiments show that algorithms higher up in the hierarchy give more accurate results when they converge but tend to be less stable.
Cite
@article{arxiv.1207.1417,
title = {The DLR Hierarchy of Approximate Inference},
author = {Michal Rosen-Zvi and Michael I. Jordan and Alan Yuille},
journal= {arXiv preprint arXiv:1207.1417},
year = {2015}
}
Comments
Appears in Proceedings of the Twenty-First Conference on Uncertainty in Artificial Intelligence (UAI2005)