Related papers: Random Coordinate Langevin Monte Carlo

Irreversible and rejection-free Monte Carlo methods, recently developed in Physics under the name Event-Chain and known in Statistics as Piecewise Deterministic Monte Carlo (PDMC), have proven to produce clear acceleration over standard…

We propose a new computationally efficient sampling scheme for Bayesian inference involving high dimensional probability distributions. Our method maps the original parameter space into a low-dimensional latent space, explores the latent…

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…

Riemannian manifold Hamiltonian Monte Carlo (RMHMC) is a powerful method of Bayesian inference that exploits underlying geometric information of the posterior distribution in order to efficiently traverse the parameter space. However, the…

Riemann manifold Hamiltonian Monte Carlo (RMHMC) has the potential to produce high-quality Markov chain Monte Carlo-output even for very challenging target distributions. To this end, a symmetric positive definite scaling matrix for RMHMC,…

One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a…

In this paper, we address the challenge of Markov Chain Monte Carlo (MCMC) algorithms within the approximate Bayesian Computation (ABC) framework, which often get trapped in local optima due to their inherent local exploration mechanism. We…

Continuous level Monte Carlo is an unbiased, continuous version of the celebrated multilevel Monte Carlo method. The approximation level is assumed to be continuous resulting in a stochastic process describing the quantity of interest.…

The problem of optimising functions with intractable gradients frequently arise in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation…

Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…

This paper introduces the R package sgmcmc; which can be used for Bayesian inference on problems with large datasets using stochastic gradient Markov chain Monte Carlo (SGMCMC). Traditional Markov chain Monte Carlo (MCMC) methods, such as…

Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior…

Hamiltonian Monte Carlo (HMC) algorithms which combine numerical approximation of Hamiltonian dynamics on finite intervals with stochastic refreshment and Metropolis correction are popular sampling schemes, but it is known that they may…

Markov Chain Monte Carlo (MCMC) sampling is computationally expensive, especially for complex models. Alternative methods make simplifying assumptions about the posterior to reduce computational burden, but their impact on predictive…

We show that for any multiple-try Metropolis algorithm, one can always accept the proposal and evaluate the importance weight that is needed to correct for the bias without extra computational cost. This results in a general, convenient,…

This paper considers the problem of optimizing the average tracking error for an elliptic partial differential equation with an uncertain lognormal diffusion coefficient. In particular, the application of the multilevel quasi-Monte Carlo…

We present a significant advancement in the field of Langevin Monte Carlo (LMC) methods by introducing the Inexact Proximal Langevin Algorithm (IPLA). This novel algorithm broadens the scope of problems that LMC can effectively address…

This article reviews the application of advanced Monte Carlo techniques in the context of Multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations which can be biased in some sense, for instance, by using the…

We discuss a Monte Carlo Markov Chain (MCMC) procedure for the random sampling of some one-dimensional lattice paths with constraints, for various constraints. We show that an approach inspired by optimal transport allows us to bound…

Classically, the continuous-time Langevin diffusion converges exponentially fast to its stationary distribution $\pi$ under the sole assumption that $\pi$ satisfies a Poincar\'e inequality. Using this fact to provide guarantees for the…