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We develop a novel class of MCMC algorithms based on a stochastized Nesterov scheme. With an appropriate addition of noise, the result is a time-inhomogeneous underdamped Langevin equation, which we prove emits a specified target…

Computational Engineering, Finance, and Science · Computer Science 2023-11-29 Duy H. Thai , Alexander L. Young , David B. Dunson

For a learning automaton, a proper configuration of its learning parameters, which are crucial for the automaton's performance, is relatively difficult due to the necessity of a manual parameter tuning before real applications. To ensure a…

Machine Learning · Computer Science 2017-11-29 Hao Ge

In this article, we study the problem of sampling from distributions whose densities are not necessarily smooth nor logconcave. We propose a simple Langevin-based algorithm that does not rely on popular but computationally challenging…

Machine Learning · Statistics 2025-12-02 Tim Johnston , Iosif Lytras , Nikolaos Makras , Sotirios Sabanis

Performing numerical integration when the integrand itself cannot be evaluated point-wise is a challenging task that arises in statistical analysis, notably in Bayesian inference for models with intractable likelihood functions. Markov…

Computation · Statistics 2020-06-17 Lawrence Middleton , George Deligiannidis , Arnaud Doucet , Pierre E. Jacob

Preconditioning of a linear system obtained from spectral discretization of time-dependent PDEs often results in a full matrix which is expensive to compute and store specially when the problem size increases. A matrix-free implementation…

Statistics Theory · Mathematics 2016-06-09 A. Ghasemi , L. K. Taylor

We establish conditions under which Metropolis-Hastings (MH) algorithms with a position-dependent proposal covariance matrix will or will not have the geometric rate of convergence. Some of the diffusions based MH algorithms like the…

Methodology · Statistics 2022-08-23 Vivekananda Roy , Lijin Zhang

We establish sample complexity guarantees for estimating the covariance matrix of a strongly log-concave smooth distribution using the unadjusted Langevin algorithm (ULA). We quantitatively compare our complexity estimates on single-chain…

Probability · Mathematics 2026-02-16 Shogo Nakakita

We introduce a new family of MCMC samplers that combine auxiliary variables, Gibbs sampling and Taylor expansions of the target density. Our approach permits the marginalisation over the auxiliary variables yielding marginal samplers, or…

Machine Learning · Statistics 2018-01-26 Michalis K. Titsias , Omiros Papaspiliopoulos

We consider the problem of sampling from a high-dimensional target distribution $\pi_\beta$ on $\mathbb{R}^d$ with density proportional to $\theta\mapsto e^{-\beta U(\theta)}$ using explicit numerical schemes based on discretising the…

Probability · Mathematics 2024-06-13 Ariel Neufeld , Matthew Ng Cheng En , Ying Zhang

In this paper, we examine the computational complexity of sampling from a Bayesian posterior (or pseudo-posterior) using the Metropolis-adjusted Langevin algorithm (MALA). MALA first employs a discrete-time Langevin SDE to propose a new…

Statistics Theory · Mathematics 2024-05-10 Rong Tang , Yun Yang

We consider the sampling problem, where the aim is to draw samples from a distribution whose density is known only up to a normalization constant. Recent breakthroughs in generative modeling to approximate a high-dimensional data…

In sampling tasks, it is common for target distributions to be known up to a normalizing constant. However, in many situations, even evaluating the unnormalized distribution can be costly or infeasible. This issue arises in scenarios such…

Computation · Statistics 2025-02-06 Wei Yuan , Guanyang Wang

Performing Bayesian inference via Markov chain Monte Carlo (MCMC) can be exceedingly expensive when posterior evaluations invoke the evaluation of a computationally expensive model, such as a system of partial differential equations. In…

Computation · Statistics 2017-12-27 Patrick Conrad , Andrew Davis , Youssef Marzouk , Natesh Pillai , Aaron Smith

In this paper, we consider the numerical solution of the poroelasticity problem with stochastic properties. We present a Two-stage Markov Chain Monte Carlo method for geomechanical subsidence. In this work, we study two techniques of…

Numerical Analysis · Mathematics 2020-07-02 Maria Vasilyeva , Aleksei Tyrylgin , Donald L. Brown , Anirban Mondal

Uncertainty Quantification through Markov Chain Monte Carlo (MCMC) can be prohibitively expensive for target probability densities with expensive likelihood functions, for instance when the evaluation it involves solving a Partial…

Computation · Statistics 2020-12-11 Mikkel B. Lykkegaard , Grigorios Mingas , Robert Scheichl , Colin Fox , Tim J. Dodwell

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

A well-known first-order method for sampling from log-concave probability distributions is the Unadjusted Langevin Algorithm (ULA). This work proposes a new annealing step-size schedule for ULA, which allows to prove new convergence…

Statistics Theory · Mathematics 2020-07-03 Paul Rolland , Armin Eftekhari , Ali Kavis , Volkan Cevher

We consider stochastic optimization problems where data is drawn from a Markov chain. Existing methods for this setting crucially rely on knowing the mixing time of the chain, which in real-world applications is usually unknown. We propose…

Machine Learning · Computer Science 2023-07-14 Ron Dorfman , Kfir Y. Levy

This study introduces a computationally efficient algorithm, delayed acceptance Markov chain Monte Carlo (DA-MCMC), designed to improve posterior simulation in quasi-Bayesian inference. Quasi-Bayesian methods, which do not require fully…

Computation · Statistics 2026-02-16 Masahiro Tanaka

In this paper we study asymptotic properties of different data-augmentation-type Markov chain Monte Carlo algorithms sampling from mixture models comprising discrete as well as continuous random variables. Of particular interest to us is…

Computation · Statistics 2014-04-04 Randal Douc , Florian Maire , Jimmy Olsson