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In a Bayesian inverse problem setting, the solution consists of a posterior measure obtained by combining prior belief, information about the forward operator, and noisy observational data. This measure is most often given in terms of a…
We derive rates of contraction of posterior distributions on nonparametric models resulting from sieve priors. The aim of the paper is to provide general conditions to get posterior rates when the parameter space has a general structure,…
Trained generative models have shown remarkable performance as priors for inverse problems in imaging -- for example, Generative Adversarial Network priors permit recovery of test images from 5-10x fewer measurements than sparsity priors.…
Advances in sensing technology have made it possible to collect large volumes of high-dimensional time-series data. In fields like genetics and neuroscience, key questions concern whether directed relationships between variables can be…
Solving inverse problems in scientific and engineering fields has long been intriguing and holds great potential for many applications, yet most techniques still struggle to address issues such as high dimensionality, nonlinearity and model…
One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo…
We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By…
We consider a dictionary learning problem whose objective is to design a dictionary such that the signals admits a sparse or an approximate sparse representation over the learned dictionary. Such a problem finds a variety of applications…
Bayesian optimization is an approach to optimizing objective functions that take a long time (minutes or hours) to evaluate. It is best-suited for optimization over continuous domains of less than 20 dimensions, and tolerates stochastic…
We introduce a framework for Continual Learning (CL) based on Bayesian inference over the function space rather than the parameters of a deep neural network. This method, referred to as functional regularisation for Continual Learning,…
Bayesian inference was once a gold standard for learning with neural networks, providing accurate full predictive distributions and well calibrated uncertainty. However, scaling Bayesian inference techniques to deep neural networks is…
Given a supervised machine learning problem where the training set has been subject to a known sampling bias, how can a model be trained to fit the original dataset? We achieve this through the Bayesian inference framework by altering the…
We reinterpret multiplicative noise in neural networks as auxiliary random variables that augment the approximate posterior in a variational setting for Bayesian neural networks. We show that through this interpretation it is both efficient…
In large-scale Bayesian inverse problems, it is often necessary to apply approximate forward models to reduce the cost of forward model evaluations, while controlling approximation quality. In the context of Bayesian inverse problems with…
We study the Gaussian Process regression model in the context of training data with noise in both input and output. The presence of two sources of noise makes the task of learning accurate predictive models extremely challenging. However,…
Bayesian Generative AI (BayesGen-AI) methods are developed and applied to Bayesian computation. BayesGen-AI reconstructs the posterior distribution by directly modeling the parameter of interest as a mapping (a.k.a. deep learner) from a…
We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian techniques for estimation and inference. In particular, to improve the prediction properties of…
One goal in Bayesian machine learning is to encode prior knowledge into prior distributions, to model data efficiently. We consider prior knowledge from systems of linear partial differential equations together with their boundary…
Imbalanced classification remains a pervasive challenge in machine learning, particularly when minority samples are too scarce to provide a robust discriminative boundary. In such extreme scenarios, conventional models often suffer from…
The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by deep generative networks). In this work, we study the…