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Stochastic gradients have been widely integrated into Langevin-based methods to improve their scalability and efficiency in solving large-scale sampling problems. However, the proximal sampler, which exhibits much faster convergence than…
The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky…
Equality-constrained models naturally arise in problems in which measurements are taken at different levels of resolution. The challenge in this setting is that the models usually induce a joint distribution which is intractable. Resorting…
We proposed a new technique to accelerate sampling methods for solving difficult optimization problems. Our method investigates the intrinsic connection between posterior distribution sampling and optimization with Langevin dynamics, and…
In previous work, we introduced a method for determining convergence rates for integration methods for the kinetic Langevin equation for $M$-$\nabla$Lipschitz $m$-log-concave densities [arXiv:2302.10684, 2023]. In this article, we exploit…
Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…
An effective approach for sampling from unnormalized densities is based on the idea of gradually transporting samples from an easy prior to the complicated target distribution. Two popular methods are (1) Sequential Monte Carlo (SMC), where…
In the context of Bayesian inversion for scientific and engineering modeling, Markov chain Monte Carlo sampling strategies are the benchmark due to their flexibility and robustness in dealing with arbitrary posterior probability density…
In a non supervised Bayesian estimation approach for inverse problems in imaging systems, one tries to estimate jointly the unknown image pixels $f$ and the hyperparameters $\theta$ given the observed data $g$ and a model $M$ linking these…
A new fast Bayesian approach is introduced for the detection of discrete objects immersed in a diffuse background. This new method, called PowellSnakes, speeds up traditional Bayesian techniques by: i) replacing the standard form of the…
We propose a reflection-free Langevin framework for sampling and optimization on compact polyhedra. The method is based on the inverse Hessian of the logarithmic barrier, which defines a Dikin--Langevin diffusion whose drift and noise adapt…
Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…
Sampling from score-based diffusion models incurs bias due to both time discretisation and the approximation of the score function. A common strategy for reducing this bias is to apply corrector steps based on the unadjusted Langevin…
We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…
Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…
We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art…
We consider the problem of sampling from constrained distributions, which has posed significant challenges to both non-asymptotic analysis and algorithmic design. We propose a unified framework, which is inspired by the classical mirror…
This paper presents a Markov chain Monte Carlo method to generate approximate posterior samples in retrospective multiple changepoint problems where the number of changes is not known in advance. The method uses conjugate models whereby the…
This paper presents a control variate-based Markov chain Monte Carlo algorithm for efficient sampling from the probability simplex, with a focus on applications in large-scale Bayesian models such as latent Dirichlet allocation. Standard…
A major interest in longitudinal neuroimaging studies involves investigating voxel-level neuroplasticity due to treatment and other factors across visits. However, traditional voxel-wise methods are beset with several pitfalls, which can…