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In ill-posed imaging inverse problems, there can exist many hypotheses that fit both the observed measurements and prior knowledge of the true image. Rather than returning just one hypothesis of that image, posterior samplers aim to explore…

Exemplar learning is a powerful paradigm for discovering visual similarities in an unsupervised manner. In this context, however, the recent breakthrough in deep learning could not yet unfold its full potential. With only a single positive…

Although freeform devices with complex internal structures promise drastic increases in performance, the discreteness of the set of available materials presents challenges for gradient-based optimization necessary for the efficient…

We provide a complete framework for performing infinite-dimensional Bayesian inference and uncertainty quantification for image reconstruction with Poisson data. In particular, we address the following issues to make the Bayesian framework…

As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…

Bayesian inference allows us to define a posterior distribution over the weights of a generic neural network (NN). Exact posteriors are usually intractable, in which case approximations can be employed. One such approximation - variational…

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…

Bayesian inverse problems highly rely on efficient and effective inference methods for uncertainty quantification (UQ). Infinite-dimensional MCMC algorithms, directly defined on function spaces, are robust under refinement of physical…

Convolutional neural networks (CNNs) work well on large datasets. But labelled data is hard to collect, and in some applications larger amounts of data are not available. The problem then is how to use CNNs with small data -- as CNNs…

Modern day engineering problems are ubiquitously characterized by sophisticated computer codes that map parameters or inputs to an underlying physical process. In other situations, experimental setups are used to model the physical process…

In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and…

We propose a novel method for sampling and optimization tasks based on a stochastic interacting particle system. We explain how this method can be used for the following two goals: (i) generating approximate samples from a given target…

This paper is concerned with inverse acoustic scattering problem of inferring the position and shape of a sound-soft obstacle from phaseless far-field data. We propose the Bayesian approach to recover sound-soft disks, line cracks and…

The class imbalance problem is important and challenging. Ensemble approaches are widely used to tackle this problem because of their effectiveness. However, existing ensemble methods are always applied into original samples, while not…

In the context of solving inverse problems for physics applications within a Bayesian framework, we present a new approach, Markov Chain Generative Adversarial Neural Networks (MCGANs), to alleviate the computational costs associated with…

Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…

We consider the problem of performing Bayesian inference for logistic regression using appropriate extensions of the ensemble Kalman filter. Two interacting particle systems are proposed that sample from an approximate posterior and prove…

Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient…

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…

The superior performance of ensemble methods with infinite models are well known. Most of these methods are based on optimization problems in infinite-dimensional spaces with some regularization, for instance, boosting methods and convex…