Related papers: Poisson Midpoint Method for Log Concave Sampling: …
In this paper, we revisit the recently established theoretical guarantees for the convergence of the Langevin Monte Carlo algorithm of sampling from a smooth and (strongly) log-concave density. We improve the existing results when the…
High-dimensional count data poses significant challenges for statistical analysis, necessitating effective methods that also preserve explainability. We focus on a low rank constrained variant of the Poisson log-normal model, which relates…
Motivated by applications to deep learning which often fail standard Lipschitz smoothness requirements, we examine the problem of sampling from distributions that are not log-concave and are only weakly dissipative, with log-gradients…
We study the underdamped Langevin dynamics with invariant measure $\mu(\,\mathrm{d}x\,\mathrm{d}v)\propto \mathrm{e}^{-U(x)-\lvert v\rvert^2/2}\,\mathrm{d}x\,\mathrm{d}v$. Assume that the position marginal $\mu_x(\,\mathrm{d}x)\propto…
We consider the fully-coupled McKean-Vlasov equation with multi-time-scale potentials, and all the coefficients depend on the distributions of both the slow component and the fast motion. By studying the smoothness of the solution of the…
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 derive first-order (in the stepsize) bounds on the bias in Wasserstein distances of the invariant measure of stochastic gradient kinetic Langevin dynamics with minimal assumptions on the stochastic gradient noise. These bounds sharpen…
In this article, we focus on the sampling of the configurational Gibbs-Boltzmann distribution, that is, the calculation of averages of functions of the position coordinates of a molecular $N$-body system modelled at constant temperature. We…
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…
A fundamental problem in Bayesian inference and statistical machine learning is to efficiently sample from multimodal distributions. Due to metastability, multimodal distributions are difficult to sample using standard Markov chain Monte…
Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear diffusion equations and prove convergence of the method…
In this paper we propose a new deterministic approximation method, called discretization approximation, for Bayesian computation. Discretization approximation is very simple to understand and to implement, It only requires calculating…
Score-based Generative Models (SGMs) aim to sample from a target distribution by learning score functions using samples perturbed by Gaussian noise. Existing convergence bounds for SGMs in the W2-distance rely on stringent assumptions about…
Bayesian methods of sampling from a posterior distribution are becoming increasingly popular due to their ability to precisely display the uncertainty of a model fit. Classical methods based on iterative random sampling and posterior…
The Stochastic Gradient Langevin Dynamics (SGLD) are popularly used to approximate Bayesian posterior distributions in statistical learning procedures with large-scale data. As opposed to many usual Markov chain Monte Carlo (MCMC)…
We study the convergence in total variation and $V$-norm of discretization schemes of the underdamped Langevin dynamics. Such algorithms are very popular and commonly used in molecular dynamics and computational statistics to…
Error bounds are derived for sampling and estimation using a discretization of an intrinsically defined Langevin diffusion with invariant measure $\text{d}\mu_\phi \propto e^{-\phi} \mathrm{dvol}_g $ on a compact Riemannian manifold. Two…
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…
In this article we consider static Bayesian parameter estimation for partially observed diffusions that are discretely observed. We work under the assumption that one must resort to discretizing the underlying diffusion process, for…
We provide full theoretical guarantees for the convergence behaviour of diffusion-based generative models under the assumption of strongly log-concave data distributions while our approximating class of functions used for score estimation…