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Efficient Adaptive MCMC Through Precision Estimation

Wallin, Jonas LU and Bolin, David LU (2018) In Journal of Computational and Graphical Statistics 27(4). p.887-897
Abstract
The performance of Markov chain Monte Carlo (MCMC) algorithms like the Metropolis Hastings Random Walk (MHRW) is highly dependent on the choice of scaling matrix for the proposal distributions. A popular choice of scaling matrix in adaptive MCMC methods is to use the empirical covariance matrix (ECM) of previous samples. However, this choice is problematic if the dimension of the target distribution is large, since the ECM then converges slowly and is computationally expensive to use. We propose two algorithms to improve convergence and decrease computational cost of adaptive MCMC methods in cases when the precision (inverse covariance) matrix of the target density can be well-approximated by a sparse matrix. The first is an algorithm for... (More)
The performance of Markov chain Monte Carlo (MCMC) algorithms like the Metropolis Hastings Random Walk (MHRW) is highly dependent on the choice of scaling matrix for the proposal distributions. A popular choice of scaling matrix in adaptive MCMC methods is to use the empirical covariance matrix (ECM) of previous samples. However, this choice is problematic if the dimension of the target distribution is large, since the ECM then converges slowly and is computationally expensive to use. We propose two algorithms to improve convergence and decrease computational cost of adaptive MCMC methods in cases when the precision (inverse covariance) matrix of the target density can be well-approximated by a sparse matrix. The first is an algorithm for online estimation of the Cholesky factor of a sparse precision matrix. The second estimates the sparsity structure of the precision matrix. Combining the two algorithms allows us to construct precision-based adaptive MCMC algorithms that can be used as black-box methods for densities with unknown dependency structures. We construct precision-based versions of the adaptive MHRW and the adaptive Metropolis adjusted Langevin algorithm and demonstrate the performance of the methods in two examples. Supplementary materials for this article are available online. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
AMCMC, Gaussian Processes
in
Journal of Computational and Graphical Statistics
volume
27
issue
4
pages
887 - 897
publisher
American Statistical Association
external identifiers
  • scopus:85052067282
ISSN
1537-2715
DOI
10.1080/10618600.2018.1459303
language
English
LU publication?
yes
id
68cbfd4a-f752-4bf6-b2af-c8b5957004f9
date added to LUP
2017-12-20 08:47:50
date last changed
2019-01-16 13:06:11
@article{68cbfd4a-f752-4bf6-b2af-c8b5957004f9,
  abstract     = {The performance of Markov chain Monte Carlo (MCMC) algorithms like the Metropolis Hastings Random Walk (MHRW) is highly dependent on the choice of scaling matrix for the proposal distributions. A popular choice of scaling matrix in adaptive MCMC methods is to use the empirical covariance matrix (ECM) of previous samples. However, this choice is problematic if the dimension of the target distribution is large, since the ECM then converges slowly and is computationally expensive to use. We propose two algorithms to improve convergence and decrease computational cost of adaptive MCMC methods in cases when the precision (inverse covariance) matrix of the target density can be well-approximated by a sparse matrix. The first is an algorithm for online estimation of the Cholesky factor of a sparse precision matrix. The second estimates the sparsity structure of the precision matrix. Combining the two algorithms allows us to construct precision-based adaptive MCMC algorithms that can be used as black-box methods for densities with unknown dependency structures. We construct precision-based versions of the adaptive MHRW and the adaptive Metropolis adjusted Langevin algorithm and demonstrate the performance of the methods in two examples. Supplementary materials for this article are available online.},
  author       = {Wallin, Jonas and Bolin, David},
  issn         = {1537-2715},
  keyword      = {AMCMC,Gaussian Processes},
  language     = {eng},
  month        = {10},
  number       = {4},
  pages        = {887--897},
  publisher    = {American Statistical Association},
  series       = {Journal of Computational and Graphical Statistics},
  title        = {Efficient Adaptive MCMC Through Precision Estimation},
  url          = {http://dx.doi.org/10.1080/10618600.2018.1459303},
  volume       = {27},
  year         = {2018},
}