Related papers: Projected Langevin Monte Carlo algorithms in non-c…
This article presents a novel and practically useful link between geometric integration, low-discrepancy sampling and code coupling for Lagrangian and Eulerian Vlasov-Poisson solvers. Low-discrepancy sequences, also called quasi-random…
Understanding the dimension dependency of computational complexity in high-dimensional sampling problem is a fundamental problem, both from a practical and theoretical perspective. Compared with samplers with unbiased stationary…
The Markov Chain Monte Carlo (MCMC) methods are popular when considering sampling from a high-dimensional random variable $\mathbf{x}$ with possibly unnormalised probability density $p$ and observed data $\mathbf{d}$. However, MCMC requires…
Bayesian Neural Networks (BNNs) provide a promising framework for modeling predictive uncertainty and enhancing out-of-distribution robustness (OOD) by estimating the posterior distribution of network parameters. Stochastic Gradient Markov…
Hamiltonian Monte Carlo and underdamped Langevin Monte Carlo are state-of-the-art methods for taking samples from high-dimensional distributions with a differentiable density function. To generate samples, they numerically integrate…
An effective approach for sampling from unnormalized densities is based on the idea of gradually transporting samples from an easy prior to the complicated target distribution. Two popular methods are (1) Sequential Monte Carlo (SMC), where…
Practitioners of Bayesian statistics have long depended on Markov chain Monte Carlo (MCMC) to obtain samples from intractable posterior distributions. Unfortunately, MCMC algorithms are typically serial, and do not scale to the large…
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…
We discuss a non-reversible, lifted Markov-chain Monte Carlo (MCMC) algorithm for particle systems in which the direction of proposed displacements is changed deterministically. This algorithm sweeps through directions analogously to the…
A higher-order change-of-measure multilevel Monte Carlo (MLMC) method is developed for computing weak approximations of the invariant measures of SDE with drift coefficients that do not satisfy the contractivity condition. This is achieved…
We propose a new method called the Metropolis-adjusted Mirror Langevin algorithm for approximate sampling from distributions whose support is a compact and convex set. This algorithm adds an accept-reject filter to the Markov chain induced…
Langevin dynamics has found a large number of applications in sampling, optimization and estimation. Preconditioning the gradient in the dynamics with the covariance - an idea that originated in literature related to solving estimation and…
We propose a multilevel Markov chain Monte Carlo (MCMC) method for the Bayesian inference of random field parameters in PDEs using high-resolution data. Compared to existing multilevel MCMC methods, we additionally consider level-dependent…
Markov chain Monte Carlo (MCMC), such as Langevin dynamics, is valid for approximating intractable distributions. However, its usage is limited in the context of deep latent variable models owing to costly datapoint-wise sampling iterations…
We present a unified framework to analyze the global convergence of Langevin dynamics based algorithms for nonconvex finite-sum optimization with $n$ component functions. At the core of our analysis is a direct analysis of the ergodicity of…
In many hierarchical inverse problems, not only do we want to estimate high- or infinite-dimensional model parameters in the parameter-to-observable maps, but we also have to estimate hyperparameters that represent critical assumptions in…
In order to solve tasks like uncertainty quantification or hypothesis tests in Bayesian imaging inverse problems, we often have to draw samples from the arising posterior distribution. For the usually log-concave but high-dimensional…
In this article we consider computing expectations w.r.t.~probability laws associated to a certain class of stochastic systems. In order to achieve such a task, one must not only resort to numerical approximation of the expectation, but…
We introduce a Markov Chain Monte Carlo (MCMC) algorithm to generate samples from probability distributions supported on a $d$-dimensional lattice $\Lambda = \mathbf{B}\mathbb{Z}^d$, where $\mathbf{B}$ is a full-rank matrix. Specifically,…
Deep learning algorithms have been widely used to solve linear Kolmogorov partial differential equations~(PDEs) in high dimensions, where the loss function is defined as a mathematical expectation. We propose to use the randomized…