Related papers: Convergence of the Riemannian Langevin Algorithm

We show how to sample in parallel from a distribution $\pi$ over $\mathbb R^d$ that satisfies a log-Sobolev inequality and has a smooth log-density, by parallelizing the Langevin (resp. underdamped Langevin) algorithms. We show that our…

The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo…

We provide a clarification of the description of Langevin diffusions on Riemannian manifolds and of the measure underlying the invariant density. As a result we propose a new position-dependent Metropolis-adjusted Langevin algorithm (MALA)…

We study the Unadjusted Langevin Algorithm (ULA) for sampling from a probability distribution $\nu = e^{-f}$ on $\mathbb{R}^n$. We prove a convergence guarantee in Kullback-Leibler (KL) divergence assuming $\nu$ satisfies a log-Sobolev…

This paper proposes a novel Bayesian framework for solving Poisson inverse problems by devising a Monte Carlo sampling algorithm which accounts for the underlying non-Euclidean geometry. To address the challenges posed by the Poisson…

We introduce adaptive, tuning-free step size schedules for gradient-based sampling algorithms obtained as time-discretizations of Wasserstein gradient flows. The result is a suite of tuning-free sampling algorithms, including tuning-free…

In this paper, we present a stochastic augmented Lagrangian approach on (possibly infinite-dimensional) Riemannian manifolds to solve stochastic optimization problems with a finite number of deterministic constraints.We investigate the…

The problem of efficiently generating random samples from high-dimensional and non-log-concave posterior measures arising from nonlinear regression problems is considered. Extending investigations from arXiv:2009.05298, local and global…

Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…

We introduce the manifold density function, which is an intrinsic method to validate manifold learning techniques. Our approach adapts and extends Ripley's $K$-function, and categorizes in an unsupervised setting the extent to which an…

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…

The stochastic gradient Langevin Dynamics is one of the most fundamental algorithms to solve sampling problems and non-convex optimization appearing in several machine learning applications. Especially, its variance reduced versions have…

This paper proposes a general framework of Riemannian adaptive optimization methods. The framework encapsulates several stochastic optimization algorithms on Riemannian manifolds and incorporates the mini-batch strategy that is often used…

We examine the Langevin diffusion confined to a closed, convex domain $D\subset\mathbb{R}^d$, represented as a reflected stochastic differential equation. We introduce a sequence of penalized stochastic differential equations and prove that…

The problem of sampling a target probability distribution on a constrained domain arises in many applications including machine learning. For constrained sampling, various Langevin algorithms such as projected Langevin Monte Carlo (PLMC),…

We introduce a novel and efficient algorithm called the stochastic approximate gradient descent (SAGD), as an alternative to the stochastic gradient descent for cases where unbiased stochastic gradients cannot be trivially obtained.…

We study the problem of sampling from a target distribution $\pi(q)\propto e^{-U(q)}$ on $\mathbb{R}^d$, where $U$ can be non-convex, via the Hessian-free high-resolution (HFHR) dynamics, which is a second-order Langevin-type process that…

We study sampling from a target distribution $\nu_* = e^{-f}$ using the unadjusted Langevin Monte Carlo (LMC) algorithm when the potential $f$ satisfies a strong dissipativity condition and it is first-order smooth with a Lipschitz…

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…

Denoising diffusion models have recently emerged as the predominant paradigm for generative modelling on image domains. In addition, their extension to Riemannian manifolds has facilitated a range of applications across the natural…