PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Quasi-Newton Methods for Markov Chain Monte Carlo
Yichuan Zhang and Charles Sutton
In: Neural Information Processing Systems Fundation, 12-18 Dec 2011, Granada, Spain.

Abstract

The performance of Markov chain Monte Carlo methods is often sensitive to the scaling and correlations between the random variables of interest. An important source of information about the local correlation and scale is given by the Hessian matrix of the target distribution, but this is often either computationally expensive or infeasible. In this paper we propose MCMC samplers that make use of quasi- Newton approximations, which approximate the Hessian of the target distribution from previous samples and gradients generated by the sampler. A key issue is that MCMC samplers that depend on the history of previous states are in general not valid. We address this problem by using limited memory quasi-Newton methods, which depend only on a fixed window of previous samples. On several real world datasets, we show that the quasi-Newton sampler is more effective than standard Hamiltonian Monte Carlo at a fraction of the cost of MCMC methods that require higher-order derivatives.

EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
ID Code:8749
Deposited By:Yichuan Zhang
Deposited On:21 February 2012