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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

Sampling logconcave functions arising in statistics and machine learning has been a subject of intensive study. Recent developments include analyses for Langevin dynamics and Hamiltonian Monte Carlo (HMC). While both approaches have…

Data Structures and Algorithms · Computer Science 2018-12-18 Yin Tat Lee , Zhao Song , Santosh S. Vempala

Metropolis-Hastings (MH) is a foundational Markov chain Monte Carlo (MCMC) algorithm. In this paper, we ask whether it is possible to formulate and analyse MH in terms of categorical probability, using a recent involutive framework for…

Computation · Statistics 2026-02-02 Rob Cornish , Andi Q. Wang

Markov Chain Monte Carlo (MCMC) algorithms play an important role in statistical inference problems dealing with intractable probability distributions. Recently, many MCMC algorithms such as Hamiltonian Monte Carlo (HMC) and Riemannian…

Computation · Statistics 2017-04-19 Cheng Zhang , Babak Shahbaba , Hongkai Zhao

We study sampling from a target distribution $\nu_* = e^{-f}$ using the unadjusted Langevin Monte Carlo (LMC) algorithm when the potential $f$ satisfies a strong dissipativity condition and it is first-order smooth with a Lipschitz…

Machine Learning · Statistics 2021-07-09 Murat A. Erdogdu , Rasa Hosseinzadeh , Matthew S. Zhang

We introduce new Gaussian proposals to improve the efficiency of the standard Hastings-Metropolis algorithm in Markov chain Monte Carlo (MCMC) methods, used for the sampling from a target distribution in large dimension $d$. The improved…

Numerical Analysis · Mathematics 2016-11-28 Alain Durmus , Gareth O. Roberts , Gilles Vilmart , Konstantinos C. Zygalakis

We present a form of stratified MCMC algorithm built with non-reversible stochastic dynamics in mind. It can also be viewed as a generalization of the exact milestoning method, or form of NEUS. We prove convergence of the method under…

Probability · Mathematics 2022-02-21 Gabriel Earle , Jonathan Mattingly

Variational inference lies at the core of many state-of-the-art algorithms. To improve the approximation of the posterior beyond parametric families, it was proposed to include MCMC steps into the variational lower bound. In this work we…

Machine Learning · Statistics 2016-09-28 Christopher Wolf , Maximilian Karl , Patrick van der Smagt

While the Matrix Generalized Inverse Gaussian ($\mathcal{MGIG}$) distribution arises naturally in some settings as a distribution over symmetric positive semi-definite matrices, certain key properties of the distribution and effective ways…

Machine Learning · Statistics 2016-08-23 Farideh Fazayeli , Arindam Banerjee

Riemannian manifold Hamiltonian Monte Carlo (RMHMC) is a sampling algorithm that seeks to adapt proposals to the local geometry of the posterior distribution. The specific form of the Hamiltonian used in RMHMC necessitates {\it…

Computation · Statistics 2021-11-22 James A. Brofos , Roy R. Lederman

Stochastic gradient Markov Chain Monte Carlo (SGMCMC) is considered the gold standard for Bayesian inference in large-scale models, such as Bayesian neural networks. Since practitioners face speed versus accuracy tradeoffs in these models,…

Machine Learning · Computer Science 2022-07-19 Antonios Alexos , Alex Boyd , Stephan Mandt

We consider the outstanding problem of sampling from an unnormalized density that may be non-log-concave and multimodal. To enhance the performance of simple Markov chain Monte Carlo (MCMC) methods, techniques of annealing type have been…

Machine Learning · Statistics 2025-02-18 Wei Guo , Molei Tao , Yongxin Chen

Recently, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) methods have been proposed for scaling up Monte Carlo computations to large data problems. Whilst these approaches have proven useful in many applications, vanilla SG-MCMC…

Machine Learning · Statistics 2016-12-13 Umut Şimşekli , Roland Badeau , A. Taylan Cemgil , Gaël Richard

Markov Chain Monte Carlo (MCMC) methods have a drawback when working with a target distribution or likelihood function that is computationally expensive to evaluate, specially when working with big data. This paper focuses on…

Machine Learning · Computer Science 2019-10-22 Asif J. Chowdhury , Gabriel Terejanu

Existing rigorous convergence guarantees for the Hamiltonian Monte Carlo (HMC) algorithm use Gaussian auxiliary momentum variables, which are crucially symmetrically distributed. We present a novel convergence analysis for HMC utilizing new…

Machine Learning · Statistics 2026-05-12 Soumyadip Ghosh , Yingdong Lu , Tomasz Nowicki

In this paper, we propose irreversible versions of the Metropolis Hastings (MH) and Metropolis adjusted Langevin algorithm (MALA) with a main focus on the latter. For the former, we show how one can simply switch between different proposal…

Methodology · Statistics 2018-03-14 Yi-An Ma , Emily B. Fox , Tianqi Chen , Lei Wu

Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement,…

Computation · Statistics 2017-03-08 Alexandros Beskos , Mark Girolami , Shiwei Lan , Patrick E. Farrell , Andrew M. Stuart

Particle MCMC is a class of algorithms that can be used to analyse state-space models. They use MCMC moves to update the parameters of the models, and particle filters to propose values for the path of the state-space model. Currently the…

Computation · Statistics 2014-12-25 Chris Nemeth , Paul Fearnhead

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

Markov chain Monte Carlo (MCMC) algorithms have become powerful tools for Bayesian inference. However, they do not scale well to large-data problems. Divide-and-conquer strategies, which split the data into batches and, for each batch, run…

Computation · Statistics 2017-07-18 Christopher Nemeth , Chris Sherlock