English
Related papers

Related papers: Fast Langevin based algorithm for MCMC in high dim…

200 papers

Sampling with Markov chain Monte Carlo methods often amounts to discretizing some continuous-time dynamics with numerical integration. In this paper, we establish the convergence rate of sampling algorithms obtained by discretizing smooth…

Machine Learning · Statistics 2020-02-04 Xuechen Li , Denny Wu , Lester Mackey , Murat A. Erdogdu

This paper considers Bayesian parameter estimation of dynamic systems using a Markov Chain Monte Carlo (MCMC) approach. The Metroplis-Hastings (MH) algorithm is employed, and the main contribution of the paper is to examine and illustrate…

Applications · Statistics 2021-10-18 Johannes Hendriks , Adrian Wills , Brett Ninness , Johan Dahlin

Pseudo-marginal Markov chain Monte Carlo methods for sampling from intractable distributions have gained recent interest and have been theoretically studied in considerable depth. Their main appeal is that they are exact, in the sense that…

Computation · Statistics 2015-03-25 Felipe J. Medina-Aguayo , Anthony Lee , Gareth O. Roberts

The problem of optimally scaling the proposal distribution in a Markov chain Monte Carlo algorithm is critical to the quality of the generated samples. Much work has gone into obtaining such results for various Metropolis-Hastings (MH)…

Computation · Statistics 2022-02-07 Sanket Agrawal , Dootika Vats , Krzysztof Łatuszyński , Gareth O. Roberts

We study the computational complexity of Markov chain Monte Carlo (MCMC) methods for high-dimensional Bayesian linear regression under sparsity constraints. We first show that a Bayesian approach can achieve variable-selection consistency…

Statistics Theory · Mathematics 2015-06-01 Yun Yang , Martin J. Wainwright , Michael I. Jordan

Performing exact Bayesian inference for complex models is computationally intractable. Markov chain Monte Carlo (MCMC) algorithms can provide reliable approximations of the posterior distribution but are expensive for large datasets and…

Computation · Statistics 2021-12-09 Maxime Vono , Daniel Paulin , Arnaud Doucet

In this paper, we study the problem of sampling from a given probability density function that is known to be smooth and strongly log-concave. We analyze several methods of approximate sampling based on discretizations of the (highly…

Statistics Theory · Mathematics 2024-02-26 Arnak S. Dalalyan , Avetik G. Karagulyan

Sampling from a high-dimensional probability distribution is a fundamental algorithmic task arising in wide-ranging applications across multiple disciplines, including scientific computing, computational statistics and machine learning.…

Statistics Theory · Mathematics 2026-05-11 Bin Yang , Xiaojie Wang

We study the efficiency of Thompson sampling for contextual bandits. Existing Thompson sampling-based algorithms need to construct a Laplace approximation (i.e., a Gaussian distribution) of the posterior distribution, which is inefficient…

Machine Learning · Computer Science 2022-06-23 Pan Xu , Hongkai Zheng , Eric Mazumdar , Kamyar Azizzadenesheli , Anima Anandkumar

We introduce Markov chain Monte Carlo (MCMC) algorithms based on numerical approximations of piecewise-deterministic Markov processes obtained with the framework of splitting schemes. We present unadjusted as well as adjusted algorithms,…

Probability · Mathematics 2025-11-04 Andrea Bertazzi , Paul Dobson , Pierre Monmarché

Federated learning performed by a decentralized networks of agents is becoming increasingly important with the prevalence of embedded software on autonomous devices. Bayesian approaches to learning benefit from offering more information as…

Machine Learning · Computer Science 2021-07-16 Vyacheslav Kungurtsev , Adam Cobb , Tara Javidi , Brian Jalaian

Langevin Monte Carlo (LMC) and its stochastic gradient versions are powerful algorithms for sampling from complex high-dimensional distributions. To sample from a distribution with density $\pi(\theta)\propto \exp(-U(\theta)) $, LMC…

Computation · Statistics 2023-09-25 Sifan Liu

We prove explicit, i.e., non-asymptotic, error bounds for Markov Chain Monte Carlo methods, such as the Metropolis algorithm. The problem is to compute the expectation (or integral) of f with respect to a measure which can be given by a…

Numerical Analysis · Mathematics 2011-01-18 Daniel Rudolf

In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…

Machine Learning · Computer Science 2022-02-11 Jiaming Liang , Yongxin Chen

Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying computational complexity. In particular, they lead directly to precise estimates of the number of steps required to explore the target…

Probability · Mathematics 2012-10-05 Jonathan C. Mattingly , Natesh S. Pillai , Andrew M. Stuart

MCMC algorithms such as Metropolis-Hastings algorithms are slowed down by the computation of complex target distributions as exemplified by huge datasets. We offer in this paper an approach to reduce the computational costs of such…

Computation · Statistics 2014-06-11 Marco Banterle , Clara Grazian , Christian P. Robert

We introduce a gradient-based learning method to automatically adapt Markov chain Monte Carlo (MCMC) proposal distributions to intractable targets. We define a maximum entropy regularised objective function, referred to as generalised speed…

Machine Learning · Statistics 2020-01-07 Michalis K. Titsias , Petros Dellaportas

Uncertainty estimation is a key issue when considering the application of deep neural network methods in science and engineering. In this work, we introduce a novel algorithm that quantifies epistemic uncertainty via Monte Carlo sampling…

Machine Learning · Statistics 2024-12-06 Sebastian Bieringer , Gregor Kasieczka , Maximilian F. Steffen , Mathias Trabs

Markov Chain Monte Carlo (MCMC) is one of the most powerful methods to sample from a given probability distribution, of which the Metropolis Adjusted Langevin Algorithm (MALA) is a variant wherein the gradient of the distribution is used…

Applications · Statistics 2022-01-21 Mariya Mamajiwala , Debasish Roy , Serge Guillas

We consider the efficient use of an approximation within Markov chain Monte Carlo (MCMC), with subsequent importance sampling (IS) correction of the Markov chain inexact output, leading to asymptotically exact inference. We detail…

Computation · Statistics 2019-04-15 Jordan Franks