相关论文: Sharp convergence rates for Langevin dynamics in t…
A new (unadjusted) Langevin Monte Carlo (LMC) algorithm with improved rates in total variation and in Wasserstein distance is presented. All these are obtained in the context of sampling from a target distribution $\pi$ that has a density…
We study the problem of sampling from a probability distribution $\pi$ on $\rset^d$ which has a density \wrt\ the Lebesgue measure known up to a normalization factor $x \mapsto \rme^{-U(x)} / \int_{\rset^d} \rme^{-U(y)} \rmd y$. We analyze…
We consider the problem of sampling from constrained distributions, which has posed significant challenges to both non-asymptotic analysis and algorithmic design. We propose a unified framework, which is inspired by the classical mirror…
Sampling from a high-dimensional probability distribution is a fundamental algorithmic task arising in wide-ranging applications across multiple disciplines, including scientific computing, computational statistics and machine learning.…
Discretized Langevin diffusions are efficient Monte Carlo methods for sampling from high dimensional target densities that are log-Lipschitz-smooth and (strongly) log-concave. In particular, the Euclidean Langevin Monte Carlo sampling…
This article considers the popular MCMC method of unadjusted Langevin Monte Carlo (LMC) and provides a non-asymptotic analysis of its sampling error in 2-Wasserstein distance. The proof is based on a refinement of mean-square analysis in Li…
The Underdamped Langevin Monte Carlo (ULMC) is a popular Markov chain Monte Carlo sampling method. It requires the computation of the full gradient of the log-density at each iteration, an expensive operation if the dimension of the problem…
The task of sampling from a high-dimensional distribution $\pi$ on $\R^d$ is a fundamental algorithmic problem with applications throughout statistics, engineering, and the sciences. Consider the Langevin diffusion on $\R^d$ \begin{align*}…
Discretization of continuous-time diffusion processes is a widely recognized method for sampling. However, it seems to be a considerable restriction when the potentials are often required to be smooth (gradient Lipschitz). This paper…
Langevin algorithms are gradient descent methods with additive noise. They have been used for decades in Markov chain Monte Carlo (MCMC) sampling, optimization, and learning. Their convergence properties for unconstrained non-convex…
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…
In this note, we consider the underdamped Langevin dynamics with invariant measure $\mu(\mathrm{d}x\,\mathrm{d}v) \propto e^{-U(x)-|v|^2/2}\,\mathrm{d}x\,\mathrm{d}v$. Assume that the position marginal $\mu_x(\mathrm{d}x)\propto…
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…
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…
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…
We consider the problem of sampling from a target distribution, which is \emph {not necessarily logconcave}, in the context of empirical risk minimization and stochastic optimization as presented in Raginsky et al. (2017). Non-asymptotic…
Langevin Monte Carlo (LMC) is a popular Bayesian sampling method. For the log-concave distribution function, the method converges exponentially fast, up to a controllable discretization error. However, the method requires the evaluation of…
Priors with non-smooth log-densities, such as the l1-prior, are widely used in Bayesian inverse problems for their sparsity-inducing properties. Existing Langevin-based sampling methods typically rely on proximal mappings or smooth…
In this paper, we study the problem of sampling from log-concave distributions supported on convex, compact sets, with a particular focus on the randomized midpoint discretization of both vanilla and kinetic Langevin diffusions in this…
In this article, we study the problem of sampling from distributions whose densities are not necessarily smooth nor logconcave. We propose a simple Langevin-based algorithm that does not rely on popular but computationally challenging…