Stereographic Markov Chain Monte Carlo

Publikation: Working paper › Preprint › Forskning

Standard

Stereographic Markov Chain Monte Carlo. / Yang, Jun; Łatuszyński, Krzysztof; Roberts, Gareth O.

arXiv preprint, 2022.

Publikation: Working paper › Preprint › Forskning

Harvard

Yang, J, Łatuszyński, K & Roberts, GO 2022 'Stereographic Markov Chain Monte Carlo' arXiv preprint.

APA

Yang, J., Łatuszyński, K., & Roberts, G. O. (2022). Stereographic Markov Chain Monte Carlo. arXiv preprint.

Vancouver

Yang J, Łatuszyński K, Roberts GO. Stereographic Markov Chain Monte Carlo. arXiv preprint. 2022 maj 24.

Author

Yang, Jun ; Łatuszyński, Krzysztof ; Roberts, Gareth O. / Stereographic Markov Chain Monte Carlo. arXiv preprint, 2022.

Bibtex

@techreport{b8be311c6163434ab6a0163aee223f4d,
title = "Stereographic Markov Chain Monte Carlo",
abstract = "High dimensional distributions, especially those with heavy tails, are notoriously difficult for off-the-shelf MCMC samplers: the combination of unbounded state spaces, diminishing gradient information, and local moves, results in empirically observed {"}stickiness{"} and poor theoretical mixing properties -- lack of geometric ergodicity. In this paper, we introduce a new class of MCMC samplers that map the original high dimensional problem in Euclidean space onto a sphere and remedy these notorious mixing problems. In particular, we develop random-walk Metropolis type algorithms as well as versions of Bouncy Particle Sampler that are uniformly ergodic for a large class of light and heavy-tailed distributions and also empirically exhibit rapid convergence in high dimensions. In the best scenario, the proposed samplers can enjoy the ``blessings of dimensionality'' that the mixing time decreases with dimension.",
keywords = "stat.CO, stat.ME, stat.ML",
author = "Jun Yang and Krzysztof {\L}atuszy{\'n}ski and Roberts, {Gareth O.}",
note = "86 pages",
year = "2022",
month = may,
day = "24",
language = "Udefineret/Ukendt",
publisher = "arXiv preprint",
type = "WorkingPaper",
institution = "arXiv preprint",

}

RIS

TY - UNPB

T1 - Stereographic Markov Chain Monte Carlo

AU - Yang, Jun

AU - Łatuszyński, Krzysztof

AU - Roberts, Gareth O.

N1 - 86 pages

PY - 2022/5/24

Y1 - 2022/5/24

N2 - High dimensional distributions, especially those with heavy tails, are notoriously difficult for off-the-shelf MCMC samplers: the combination of unbounded state spaces, diminishing gradient information, and local moves, results in empirically observed "stickiness" and poor theoretical mixing properties -- lack of geometric ergodicity. In this paper, we introduce a new class of MCMC samplers that map the original high dimensional problem in Euclidean space onto a sphere and remedy these notorious mixing problems. In particular, we develop random-walk Metropolis type algorithms as well as versions of Bouncy Particle Sampler that are uniformly ergodic for a large class of light and heavy-tailed distributions and also empirically exhibit rapid convergence in high dimensions. In the best scenario, the proposed samplers can enjoy the ``blessings of dimensionality'' that the mixing time decreases with dimension.

AB - High dimensional distributions, especially those with heavy tails, are notoriously difficult for off-the-shelf MCMC samplers: the combination of unbounded state spaces, diminishing gradient information, and local moves, results in empirically observed "stickiness" and poor theoretical mixing properties -- lack of geometric ergodicity. In this paper, we introduce a new class of MCMC samplers that map the original high dimensional problem in Euclidean space onto a sphere and remedy these notorious mixing problems. In particular, we develop random-walk Metropolis type algorithms as well as versions of Bouncy Particle Sampler that are uniformly ergodic for a large class of light and heavy-tailed distributions and also empirically exhibit rapid convergence in high dimensions. In the best scenario, the proposed samplers can enjoy the ``blessings of dimensionality'' that the mixing time decreases with dimension.

KW - stat.CO

KW - stat.ME

KW - stat.ML

M3 - Preprint

BT - Stereographic Markov Chain Monte Carlo

PB - arXiv preprint

ER -

ID: 361432294