Related papers: Efficient Approximate Posterior Sampling with Anne…
Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to…
Deep generative modeling has led to new and state of the art approaches for enforcing structural priors in a variety of inverse problems. In contrast to priors given by sparsity, deep models can provide direct low-dimensional…
We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach…
A Monte Carlo algorithm is said to be adaptive if it automatically calibrates its current proposal distribution using past simulations. The choice of the parametric family that defines the set of proposal distributions is critical for good…
From a Bayesian perspective, score-based diffusion solves inverse problems through joint inference, embedding the likelihood with the prior to guide the sampling process. However, this formulation fails to explain its practical behavior:…
Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modeling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by…
Slice sampling is a well-established Markov chain Monte Carlo method for (approximate) sampling of target distributions which are only known up to a normalizing constant. The method is based on choosing a new state on a slice, i.e., a…
The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such as Markov chain Monte Carlo, for which the generation of each sample requires one or more evaluations of the parameter-to-observable map or…
In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…
Stochastic gradient Markov Chain Monte Carlo algorithms are popular samplers for approximate inference, but they are generally biased. We show that many recent versions of these methods (e.g. Chen et al. (2014)) cannot be corrected using…
This paper investigates a novel a-posteriori variance reduction approach in Monte Carlo image synthesis. Unlike most established methods based on lateral filtering in the image space, our proposition is to produce the best possible estimate…
In this paper, we examine the computational complexity of sampling from a Bayesian posterior (or pseudo-posterior) using the Metropolis-adjusted Langevin algorithm (MALA). MALA first employs a discrete-time Langevin SDE to propose a new…
We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where…
The Bayesian approach to inverse problems provides a rigorous framework for the incorporation and quantification of uncertainties in measurements, parameters and models. We are interested in designing numerical methods which are robust…
Posterior sampling is a task of central importance in Bayesian inference. For many applications in Bayesian meta-analysis and Bayesian transfer learning, the prior distribution is unknown and needs to be estimated from samples. In practice,…
This work presents a tractable approach to multi-object posterior computation under a generic measurement likelihood function. While filtering is a popular solution, valuable historical information is discarded. Posterior inference, which…
Tomographic imaging is in general an ill-posed inverse problem. Typically, a single regularized image estimate of the sought-after object is obtained from tomographic measurements. However, there may be multiple objects that are all…
We study zeroth-order optimization where solutions must minimize a cost $d(s)$ while maintaining high probability under a complex generative prior $L(s)$ (e.g., a parameterized model). This reduces to sampling from a target distribution…
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…
In this paper, we propose an efficient pseudo-marginal Markov chain Monte Carlo (MCMC) sampling approach to draw samples from posterior shape distributions for image segmentation. The computation time of the proposed approach is independent…