Related papers: Posterior Sampling in High Dimension via Diffusion…

Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and…

Recent studies demonstrate that diffusion models can serve as a strong prior for solving inverse problems. A prominent example is Diffusion Posterior Sampling (DPS), which approximates the posterior distribution of data given the measure…

High-dimensional data are routinely collected in many areas. We are particularly interested in Bayesian classification models in which one or more variables are imbalanced. Current Markov chain Monte Carlo algorithms for posterior…

Modern applications routinely collect high-dimensional data, leading to statistical models having more parameters than there are samples available. A common solution is to impose sparsity in parameter estimation, often using penalized…

This paper explores the use of score-based diffusion models for Bayesian image reconstruction. Diffusion models are an efficient tool for generative modeling. Diffusion models can also be used for solving image reconstruction problems. We…

Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…

In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes' formula, giving rise…

In the field of inverse estimation for systems modeled by partial differential equations (PDEs), challenges arise when estimating high- (or even infinite-) dimensional parameters. Typically, the ill-posed nature of such problems…

Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the…

Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…

Diffusion models have recently shown considerable potential in solving Bayesian inverse problems when used as priors. However, sampling from the resulting denoising posterior distributions remains a challenge as it involves intractable…

Score-based diffusion models are a recently developed framework for posterior sampling in Bayesian inverse problems with a state-of-the-art performance for severely ill-posed problems by leveraging a powerful prior distribution learned from…

Poisson log-linear models are ubiquitous in many applications, and one of the most popular approaches for parametric count regression. In the Bayesian context, however, there are no sufficient specific computational tools for efficient…

We consider the problem of scalable sampling algorithms to fit Bayesian generalized linear mixed models on large datasets. Stochastic gradient Langevin dynamics, coupled with smooth re-parameterizations of variance parameters, produces…

Diffusion models have emerged as a powerful foundation model for visual generations. With an appropriate sampling process, it can effectively serve as a generative prior for solving general inverse problems. Current posterior sampling-based…

We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…

Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…

Stochastic differential equations (SDEs) or diffusions are continuous-valued continuous-time stochastic processes widely used in the applied and mathematical sciences. Simulating paths from these processes is usually an intractable problem,…

Diffusion posterior sampling solves inverse problems by combining a pretrained diffusion prior with measurement-consistency guidance, but it often fails to recover fine details because measurement terms are applied in a manner that is…

We propose an algorithm for the efficient and robust sampling of the posterior probability distribution in Bayesian inference problems. The algorithm combines the local search capabilities of the Manifold Metropolis Adjusted Langevin…