Related papers: On stochastic gradient Langevin dynamics with depe…
In this work, we investigate the convergence properties of the backward regularized Wasserstein proximal (BRWP) method for sampling a target distribution. The BRWP approach can be shown as a semi-implicit time discretization for a…
Langevin Dynamics is a Stochastic Differential Equation (SDE) central to sampling and generative modeling and is implemented via time discretization. Langevin Monte Carlo (LMC), based on the Euler-Maruyama discretization, is the simplest…
We prove, under mild conditions, that the stochastic gradient Langevin dynamics converges to a limiting law as time tends to infinity, even in the case where the driving data sequence is dependent.
We establish normal approximation in the Wasserstein metric for both non-degenerate and degenerate second-order U-statistics under cross-sectional dependence using Stein's method. For the non-degenerate case, our results extend recent…
Constrained sampling is an important and challenging task in computational statistics, concerned with generating samples from a distribution under certain constraints. There are numerous types of algorithm aimed at this task, ranging from…
We study the particle method to approximate the gradient flow on the $L^p$-Wasserstein space. This method relies on the discretization of the energy introduced by [3] via nonoverlapping balls centered at the particles and preserves the…
This paper concerns an optimization algorithm for unconstrained non-convex problems where the objective function has sparse connections between the unknowns. The algorithm is based on applying a dissipation preserving numerical integrator,…
We build a new class of generative algorithms capable of efficiently learning an arbitrary target distribution from possibly scarce, high-dimensional data and subsequently generate new samples. These generative algorithms are particle-based…
We propose a method for estimating a log-concave density on $\mathbb R^d$ from samples, under the assumption that there exists an orthogonal transformation that makes the components of the random vector independent. While log-concave…
Various differentially private algorithms instantiate the exponential mechanism, and require sampling from the distribution $\exp(-f)$ for a suitable function $f$. When the domain of the distribution is high-dimensional, this sampling can…
In applications of Gaussian processes where quantification of uncertainty is of primary interest, it is necessary to accurately characterize the posterior distribution over covariance parameters. This paper proposes an adaptation of the…
We introduce a theoretical framework for sampling from unnormalized densities based on a smoothing scheme that uses an isotropic Gaussian kernel with a single fixed noise scale. We prove one can decompose sampling from a density (minimal…
Simulating the kinetic Langevin dynamics is a popular approach for sampling from distributions, where only their unnormalized densities are available. Various discretizations of the kinetic Langevin dynamics have been considered, where the…
We present and study a novel algorithm for the computation of 2-Wasserstein population barycenters of absolutely continuous probability measures on Euclidean space. The proposed method can be seen as a stochastic gradient descent procedure…
Score-based Generative Models (SGMs) approximate a data distribution by perturbing it with Gaussian noise and subsequently denoising it via a learned reverse diffusion process. These models excel at modeling complex data distributions and…
We study sampling as optimization in the space of measures. We focus on gradient flow-based optimization with the Langevin dynamics as a case study. We investigate the source of the bias of the unadjusted Langevin algorithm (ULA) in…
Convergence of the gradient descent algorithm has been attracting renewed interest due to its utility in deep learning applications. Even as multiple variants of gradient descent were proposed, the assumption that the gradient of the…
When propagating uncertainty in the data of differential equations, the probability laws describing the uncertainty are typically themselves subject to uncertainty. We present a sensitivity analysis of uncertainty propagation for…
Acceleration is a celebrated cornerstone of convex optimization, enabling gradient-based algorithms to converge sublinearly in the condition number. A major open question is whether an analogous acceleration phenomenon is possible for…
We present a tensor train (TT) based algorithm designed for sampling from a target distribution and employ TT approximation to capture the high-dimensional probability density evolution of overdamped Langevin dynamics. This involves…