相关论文: High-dimensional MCMC with a standard splitting sc…
Langevin MCMC gradient optimization is a class of increasingly popular methods for estimating a posterior distribution. This paper addresses the algorithm as applied in a decentralized setting, wherein data is distributed across a network…
This work considers the problem of sampling from a probability distribution known up to a normalization constant while satisfying a set of statistical constraints specified by the expected values of general nonlinear functions. This problem…
In this work, we propose a first-order sampling method called the Metropolis-adjusted Preconditioned Langevin Algorithm for approximate sampling from a target distribution whose support is a proper convex subset of $\mathbb{R}^{d}$. Our…
In this paper, we study the problem of sampling from a given probability density function that is known to be smooth and strongly log-concave. We analyze several methods of approximate sampling based on discretizations of the (highly…
Contraction in Wasserstein 1-distance with explicit rates is established for generalized Hamiltonian Monte Carlo with stochastic gradients under possibly nonconvex conditions. The algorithms considered include splitting schemes of kinetic…
This paper provides a convergence analysis for generalized Hamiltonian Monte Carlo samplers, a family of Markov Chain Monte Carlo methods based on leapfrog integration of Hamiltonian dynamics and kinetic Langevin diffusion, that encompasses…
Algorithms based on discretizing Langevin diffusion are popular tools for sampling from high-dimensional distributions. We develop novel connections between such Monte Carlo algorithms, the theory of Wasserstein gradient flow, and the…
Non-convex sampling is a key challenge in machine learning, central to non-convex optimization in deep learning as well as to approximate probabilistic inference. Despite its significance, theoretically there remain many important…
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…
Sampling with Markov chain Monte Carlo methods often amounts to discretizing some continuous-time dynamics with numerical integration. In this paper, we establish the convergence rate of sampling algorithms obtained by discretizing smooth…
Sampling from distributions play a crucial role in aiding practitioners with statistical inference. However, in numerous situations, obtaining exact samples from complex distributions is infeasible. Consequently, researchers often turn to…
We consider a family of unadjusted generalized HMC samplers, which includes standard position HMC samplers and discretizations of the underdamped Langevin process. A detailed analysis and optimization of the parameters is conducted in the…
We study the task of efficiently sampling from a Gibbs distribution $d \pi^* = e^{-h} d {vol}_g$ over a Riemannian manifold $M$ via (geometric) Langevin MCMC; this algorithm involves computing exponential maps in random Gaussian directions…
We provide convergence guarantees in Wasserstein distance for a variety of variance-reduction methods: SAGA Langevin diffusion, SVRG Langevin diffusion and control-variate underdamped Langevin diffusion. We analyze these methods under a…
In this paper, we consider the underdamped Langevin diffusion (ULD) and propose a numerical approximation using its associated ordinary differential equation (ODE). When used as a Markov Chain Monte Carlo (MCMC) algorithm, we show that the…
Langevin algorithms are gradient descent methods augmented with additive noise, and are widely used in Markov Chain Monte Carlo (MCMC) sampling, optimization, and machine learning. In recent years, the non-asymptotic analysis of Langevin…
Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that represent the discretization of an underlying function. This work introduces a family of Markov chain Monte Carlo (MCMC)…
Nonlinear non-Gaussian state-space models arise in numerous applications in statistics and signal processing. In this context, one of the most successful and popular approximation techniques is the Sequential Monte Carlo (SMC) algorithm,…
The Metropolis-adjusted Langevin algorithm (MALA) is a Metropolis-Hastings method for approximate sampling from continuous distributions. We derive upper bounds for the contraction rate in Kantorovich-Rubinstein-Wasserstein distance of the…
We study the approximation of a (finite) continuous-time Markov chain by a Markov chain on a reduced state space, and we provide formal error bounds for the approximated transient distributions in the Wasserstein distance. These bounds…