Related papers: Optimal scaling and diffusion limits for the Lange…

We describe a new MCMC method optimized for the sampling of probability measures on Hilbert space which have a density with respect to a Gaussian; such measures arise in the Bayesian approach to inverse problems, and in conditioned…

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…

We introduce MALT: a new Metropolis adjusted sampler built upon the (kinetic) Langevin diffusion. Compared to Generalized Hamiltonian Monte Carlo (GHMC), the Metropolis correction is applied to whole Langevin trajectories, which prevents…

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…

Sampling from discrete distributions is a ubiquitous task in machine learning, recently revisited by the emergence of discrete diffusion models. While Langevin algorithms constitute the state of the art for continuous spaces, discrete…

We study sampling as optimization in the space of measures. We focus on gradient flow-based optimization with the Langevin dynamics as a case study. We investigate the source of the bias of the unadjusted Langevin algorithm (ULA) in…

In this study, we investigate the performance of the Metropolis-adjusted Langevin algorithm in a setting with constraints on the support of the target distribution. We provide a rigorous analysis of the resulting Markov chain, establishing…

Langevin dynamics are widely used in sampling high-dimensional, non-Gaussian distributions whose densities are known up to a normalizing constant. In particular, there is strong interest in unadjusted Langevin algorithms (ULA), which…

There has been considerable interest in designing Markov chain Monte Carlo algorithms by exploiting numerical methods for Langevin dynamics, which includes Hamiltonian dynamics as a deterministic case. A prominent approach is Hamiltonian…

We utilise a sampler originating from nonequilibrium statistical mechanics, termed here Jarzynski-adjusted Langevin algorithm (JALA), to build statistical estimation methods in latent variable models. We achieve this by leveraging…

We propose a new Metropolis-Hastings (MH) kernel by introducing the Mirror move into the Metropolis adjusted Langevin algorithm (MALA). This new kernel uses the strength of one kernel to overcome the shortcoming of the other, and generates…

Sampling from a high-dimensional distribution is a fundamental task in statistics, engineering, and the sciences. A canonical approach is the Langevin Algorithm, i.e., the Markov chain for the discretized Langevin Diffusion. This is the…

In this paper we perform Bayesian estimation of stochastic volatility models with heavy tail distributions using Metropolis adjusted Langevin (MALA) and Riemman manifold Langevin (MMALA) methods. We provide analytical expressions for the…

Scaling of proposals for Metropolis algorithms is an important practical problem in MCMC implementation. Criteria for scaling based on empirical acceptance rates of algorithms have been found to work consistently well across a broad range…

We examine the behaviour of the pseudo-marginal random walk Metropolis algorithm, where evaluations of the target density for the accept/reject probability are estimated rather than computed precisely. Under relatively general conditions on…

We introduce a class of algorithms, termed proximal interacting particle Langevin algorithms (PIPLA), for inference and learning in latent variable models whose joint probability density is non-differentiable. Leveraging proximal Markov…

We examine the optimal scaling and the efficiency of the pseudo-marginal random walk Metropolis algorithm using a recently-derived result on the limiting efficiency as the dimension, $d\rightarrow \infty$. We prove that the optimal scaling…

In this paper, we provide non-asymptotic upper bounds on the error of sampling from a target density using three schemes of discretized Langevin diffusions. The first scheme is the Langevin Monte Carlo (LMC) algorithm, the Euler…

One main limitation of the existing optimal scaling results for Metropolis--Hastings algorithms is that the assumptions on the target distribution are unrealistic. In this paper, we consider optimal scaling of random-walk Metropolis…

Langevin diffusion processes and their discretizations are often used for sampling from a target density. The most convenient framework for assessing the quality of such a sampling scheme corresponds to smooth and strongly log-concave…