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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…

Developing efficient Bayesian computation algorithms for imaging inverse problems is challenging due to the dimensionality involved and because Bayesian imaging models are often not smooth. Current state-of-the-art methods often address…

Bayesian neural networks (BNNs) require scalable sampling algorithms to approximate posterior distributions over parameters. Existing stochastic gradient Markov Chain Monte Carlo (SGMCMC) methods are highly sensitive to the choice of…

Sampling the parameter space of artificial neural networks according to a Boltzmann distribution provides insight into the geometry of low-loss solutions and offers an alternative to conventional loss minimization for training. However,…

We give lower bounds on the performance of two of the most popular sampling methods in practice, the Metropolis-adjusted Langevin algorithm (MALA) and multi-step Hamiltonian Monte Carlo (HMC) with a leapfrog integrator, when applied to…

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…

Despite having various attractive qualities such as high prediction accuracy and the ability to quantify uncertainty and avoid over-fitting, Bayesian Matrix Factorization has not been widely adopted because of the prohibitive cost of…

We propose an adaptive biasing algorithm aimed at enhancing the sampling of multimodal measures by Langevin dynamics. The underlying idea consists in generalizing the standard adaptive biasing force method commonly used in conjunction with…

Markov Chain Monte Carlo methods are widely used in signal processing and communications for statistical inference and stochastic optimization. In this work, we introduce an efficient adaptive Metropolis-Hastings algorithm to draw samples…

A fully Bayesian treatment of complicated predictive models (such as deep neural networks) would enable rigorous uncertainty quantification and the automation of higher-level tasks including model selection. However, the intractability of…

The discretization of overdamped Langevin dynamics, through schemes such as the Euler-Maruyama method, can be corrected by some acceptance/rejection rule, based on a Metropolis-Hastings criterion for instance. In this case, the invariant…

Stochastic Gradient Langevin Dynamics (SGLD) has emerged as a key MCMC algorithm for Bayesian learning from large scale datasets. While SGLD with decreasing step sizes converges weakly to the posterior distribution, the algorithm is often…

Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known…

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…

Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…

The Metropolis-Adjusted Langevin Algorithm (MALA) is a widely used Markov Chain Monte Carlo (MCMC) method for sampling from high-dimensional distributions. However, MALA relies on differentiability assumptions that restrict its…

This paper introduces a new Markov Chain Monte Carlo method for Bayesian variable selection in high dimensional settings. The algorithm is a Hastings-Metropolis sampler with a proposal mechanism which combines a Metropolis Adjusted Langevin…

Among random sampling methods, Markov Chain Monte Carlo algorithms are foremost. Using a combination of analytical and numerical approaches, we study their convergence properties towards the steady state, within a random walk Metropolis…

In this paper we introduce and analyse Langevin samplers that consist of perturbations of the standard underdamped Langevin dynamics. The perturbed dynamics is such that its invariant measure is the same as that of the unperturbed dynamics.…

Many methods that build powerful variational distributions based on unadjusted Langevin transitions exist. Most of these were developed using a wide range of different approaches and techniques. Unfortunately, the lack of a unified analysis…