Related papers: Speeding Up Nonsmooth Bayesian MCMC Sampling via I…

This paper presents an improved implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is based on Markov chain Monte Carlo (MCMC). However, the samples generated by…

In this paper we propose a proximal algorithm for minimizing an objective function of two block variables consisting of three terms: 1) a smooth function, 2) a nonsmooth function which is a composition between a strictly increasing,…

We present a diffusion-based image morphing approach with perceptually-uniform sampling (IMPUS) that produces smooth, direct and realistic interpolations given an image pair. The embeddings of two images may lie on distinct conditioned…

Underdamped Langevin Monte Carlo (ULMC) is an algorithm used to sample from unnormalized densities by leveraging the momentum of a particle moving in a potential well. We provide a novel analysis of ULMC, motivated by two central questions:…

Inverse imaging problems (IIPs) arise in various applications, with the main objective of reconstructing an image from its compressed measurements. This problem is often ill-posed for being under-determined with multiple interchangeably…

This work introduces a novel framework for precisely and efficiently estimating rare event probabilities in complex, high-dimensional non-Gaussian spaces, building on our foundational Approximate Sampling Target with Post-processing…

In this paper, we develop a novel distributed algorithm for addressing convex optimization with both nonlinear inequality and linear equality constraints, where the objective function can be a general nonsmooth convex function and all the…

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…

Bayesian inference with Markov Chain Monte Carlo (MCMC) is challenging when the likelihood function is irregular and expensive to compute. We explore several sampling algorithms that make use of subset evaluations to reduce computational…

Traditional measures of smoothness often fail to provide accurate $L_p$-error estimates for approximation by sampling or interpolation operators, especially for functions with low smoothness. To address this issue, we introduce a modified…

This paper focuses on a challenging class of inverse problems that is often encountered in applications. The forward model is a complex non-linear black-box, potentially non-injective, whose outputs cover multiple decades in amplitude.…

Monte Carlo simulations are widely used to simulate complex molecular systems, but standard approaches suffer from metastability. Lately, the use of non-local proposal updates in a collective-variable (CV) space has been proposed in several…

This paper develops the proximal method of multipliers for a class of nonsmooth convex optimization. The method generates a sequence of minimization problems (subproblems). We show that the sequence of approximations to the solutions of the…

In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in…

Score-based diffusion models demonstrate superior performance in generative tasks but encounter fundamental bottlenecks in inverse problems due to the analytical intractability of the time-dependent likelihood score. To bridge this gap, we…

We propose discrete Langevin proposal (DLP), a simple and scalable gradient-based proposal for sampling complex high-dimensional discrete distributions. In contrast to Gibbs sampling-based methods, DLP is able to update all coordinates in…

Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…

Large-scale Gaussian process models are becoming increasingly important and widely used in many areas, such as, computer experiments, stochastic optimization via simulation, and machine learning using Gaussian processes. The standard…

This paper proposes and develops inexact proximal methods for finding stationary points of the sum of a smooth function and a nonsmooth weakly convex one, where an error is present in the calculation of the proximal mapping of the nonsmooth…

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…