Related papers: Sampling as optimization in the space of measures:…
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…
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…
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.…
Geometric tempering is a popular approach to sampling from challenging multi-modal probability distributions by instead sampling from a sequence of distributions which interpolate, using the geometric mean, between an easier proposal…
Standard first-order Langevin algorithms such as the unadjusted Langevin algorithm (ULA) are obtained by discretizing the Langevin diffusion and are widely used for sampling in machine learning because they scale to high dimensions and…
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…
Adaptive or dynamic signal sampling in sensing systems can adapt subsequent sampling strategies based on acquired signals, thereby potentially improving image quality and speed. This paper proposes a Bayesian method for adaptive sampling…
The modified Method of Successive Approximations (MSA) is an iterative scheme for approximating solutions to stochastic control problems in continuous time based on Pontryagin Optimality Principle which, starting with an initial open loop…
Discretization of continuous-time diffusion processes is a widely recognized method for sampling. However, the canonical Euler Maruyama discretization of the Langevin diffusion process, referred as Unadjusted Langevin Algorithm (ULA),…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
The classical (overdamped) Langevin dynamics provide a natural algorithm for sampling from its invariant measure, which uniquely minimizes an energy functional over the space of probability measures, and which concentrates around the…
The primary goal of this paper is to provide an efficient solution algorithm based on the augmented Lagrangian framework for optimization problems with a stochastic objective function and deterministic constraints. Our main contribution is…
This work explores a novel perspective on solving nonconvex and nonsmooth optimization problems by leveraging sampling based methods. Instead of treating the objective function purely through traditional (often deterministic) optimization…
This work proposes a simple yet effective sampling framework for combinatorial optimization (CO). Our method builds on discrete Langevin dynamics (LD), an efficient gradient-guided generative paradigm. However, we observe that directly…
In this paper we propose a new approach for sampling from probability measures in, possibly, high dimensional spaces. By perturbing the standard overdamped Langevin dynamics by a suitable Stratonovich perturbation that preserves the…
Sampling from discrete distributions is a ubiquitous task in machine learning, recently revisited by the emergence of discrete diffusion models. While Langevin algorithms constitute the state of the art for continuous spaces, discrete…
We establish sample complexity guarantees for estimating the covariance matrix of a strongly log-concave smooth distribution using the unadjusted Langevin algorithm (ULA). We quantitatively compare our complexity estimates on single-chain…
We consider the problem of sampling from a strongly log-concave density in $\mathbb{R}^d$, and prove a non-asymptotic upper bound on the mixing time of the Metropolis-adjusted Langevin algorithm (MALA). The method draws samples by…
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 Riemannian Langevin Algorithm for the problem of sampling from a distribution with density $\nu$ with respect to the natural measure on a manifold with metric $g$. We assume that the target density satisfies a log-Sobolev…