Related papers: A variational Bayesian method for inverse problems…

Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges via a neural network that approximates the…

Bayesian hierarchical models can provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models typically comprise a conditionally Gaussian prior model for the unknown which is augmented by a generalized…

Modern machine learning applications should be able to address the intrinsic challenges arising over inference on massive real-world datasets, including scalability and robustness to outliers. Despite the multiple benefits of Bayesian…

This paper focuses on efficient computational approaches to compute approximate solutions of a linear inverse problem that is contaminated with mixed Poisson--Gaussian noise, and when there are additional outliers in the measured data. The…

In this article, we propose a novel method for sampling potential functions based on noisy observation data of a finite number of observables in quantum canonical ensembles, which leads to the accurate sampling of a wide class of test…

This paper focusses on robust estimation of location and concentration parameters of the von Mises-Fisher distribution in the Bayesian framework. The von Mises-Fisher (or Langevin) distribution has played a central role in directional…

We consider the problem of estimating the state transition matrix of a linear time-invariant (LTI) system, given access to multiple independent trajectories sampled from the system. Several recent papers have conducted a non-asymptotic…

Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…

In high-dimensional statistics, the Lasso is a cornerstone method for simultaneous variable selection and parameter estimation. However, its reliance on the squared loss function renders it highly sensitive to outliers and heavy-tailed…

We propose self-diffusion, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward…

High intensity focused ultrasound is a non-invasive method for treatment of diseased tissue that uses a beam of ultrasound to generate heat within a small volume. A common challenge in application of this technique is that heterogeneity of…

In this work we develop a Bayesian setting to infer unknown parameters in initial-boundary value problems related to linear parabolic partial differential equations. We realistically assume that the boundary data are noisy, for a given…

We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…

We consider optimal sensor placement for hyper-parameterized linear Bayesian inverse problems, where the hyper-parameter characterizes nonlinear flexibilities in the forward model, and is considered for a range of possible values. This…

We demonstrate an efficient algorithm for inverse problems in time-dependent quantum dynamics based on feedback loops between Hamiltonian parameters and the solutions of the Schr\"{o}dinger equation. Our approach formulates the inverse…

Crowdsourcing has emerged as an effective means for performing a number of machine learning tasks such as annotation and labelling of images and other data sets. In most early settings of crowdsourcing, the task involved classification,…

The conventional approach to data-driven inversion framework is based on Gaussian statistics that presents serious difficulties, especially in the presence of outliers in the measurements. In this work, we present maximum likelihood…

Considering a common case where measurements are obtained from independent sensors, we present a novel outlier-robust filter for nonlinear dynamical systems in this work. The proposed method is devised by modifying the measurement model and…

Recent advances in deep learning have brought to the fore models that can make multiple computational steps in the service of completing a task; these are capable of describ- ing long-term dependencies in sequential data. Novel recurrent…

Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…