Translator Disclaimer
April 2015 Approximation algorithms for the normalizing constant of Gibbs distributions
Mark Huber
Ann. Appl. Probab. 25(2): 974-985 (April 2015). DOI: 10.1214/14-AAP1015

Abstract

Consider a family of distributions $\{\pi_{\beta}\}$ where $X\sim\pi_{\beta}$ means that $\mathbb{P}(X=x)=\exp(-\beta H(x))/Z(\beta)$. Here $Z(\beta)$ is the proper normalizing constant, equal to $\sum_{x}\exp(-\beta H(x))$. Then $\{\pi_{\beta}\}$ is known as a Gibbs distribution, and $Z(\beta)$ is the partition function. This work presents a new method for approximating the partition function to a specified level of relative accuracy using only a number of samples, that is, $O(\ln(Z(\beta))\ln(\ln(Z(\beta))))$ when $Z(0)\geq1$. This is a sharp improvement over previous, similar approaches that used a much more complicated algorithm, requiring $O(\ln(Z(\beta))\ln(\ln(Z(\beta)))^{5})$ samples.

Citation

Download Citation

Mark Huber. "Approximation algorithms for the normalizing constant of Gibbs distributions." Ann. Appl. Probab. 25 (2) 974 - 985, April 2015. https://doi.org/10.1214/14-AAP1015

Information

Published: April 2015
First available in Project Euclid: 19 February 2015

zbMATH: 1328.65011
MathSciNet: MR3313760
Digital Object Identifier: 10.1214/14-AAP1015

Subjects:
Primary: 65C60, 68Q87
Secondary: 65C05

Rights: Copyright © 2015 Institute of Mathematical Statistics

JOURNAL ARTICLE
12 PAGES


SHARE
Vol.25 • No. 2 • April 2015
Back to Top