Related papers: Sparse Bayesian mass-mapping with uncertainties: p…
With increasingly large data sets, weak lensing measurements are able to measure cosmological parameters with ever greater precision. However this increased accuracy also places greater demands on the statistical tools used to extract the…
We have previously reported a Bayesian algorithm for determining the coordinates of points in three-dimensional space from uncertain constraints. This method is useful in the determination of biological molecular structure. It is limited,…
We study the high-dimensional inference of a rank-one signal corrupted by sparse noise. The noise is modelled as the adjacency matrix of a weighted undirected graph with finite average connectivity in the large size limit. Using the replica…
We study sparse recovery with structured random measurement matrices having independent, identically distributed, and uniformly bounded rows and with a nontrivial covariance structure. This class of matrices arises from random sampling of…
In many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional…
A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…
Bayesian coresets have emerged as a promising approach for implementing scalable Bayesian inference. The Bayesian coreset problem involves selecting a (weighted) subset of the data samples, such that the posterior inference using the…
This paper develops a new empirical Bayesian inference algorithm for solving a linear inverse problem given multiple measurement vectors (MMV) of under-sampled and noisy observable data. Specifically, by exploiting the joint sparsity across…
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…
Uncertainty quantification plays an important role in achieving trustworthy and reliable learning-based computational imaging. Recent advances in generative modeling and Bayesian neural networks have enabled the development of…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
To take full advantage of the unprecedented power of upcoming weak lensing surveys, understanding the noise, such as cosmic variance and geometry/mask effects, is as important as understanding the signal itself. Accurately quantifying the…
Reliable MRI is crucial for accurate interpretation in therapeutic and diagnostic tasks. However, undersampling during MRI acquisition as well as the overparameterized and non-transparent nature of deep learning (DL) leaves substantial…
Deep neural networks (NNs) are known to lack uncertainty estimates and struggle to incorporate new data. We present a method that mitigates these issues by converting NNs from weight space to function space, via a dual parameterization.…
In this paper we provide a statistical analysis of the parameter-free method often used in weak lensing mass reconstructions. It is found that a proper assessment of the errors involved in such a non-local analysis requires the study of the…
The Bayesian inversion method demonstrates significant potential for solving inverse problems, enabling both point estimation and uncertainty quantification (UQ). However, Bayesian maximum a posteriori (MAP) estimation may become unstable…
Recovery of support of a sparse vector from simple measurements is a widely-studied problem, considered under the frameworks of compressed sensing, 1-bit compressed sensing, and more general single index models. We consider generalizations…
In recent years, neural networks have revolutionized various domains, yet challenges such as hyperparameter tuning and overfitting remain significant hurdles. Bayesian neural networks offer a framework to address these challenges by…
We derive an estimator of weak gravitational lensing shear from background galaxy images that avoids noise-induced biases through a rigorous Bayesian treatment of the measurement. The derived shear estimator disposes with the assignment of…
We present a new method to extract cosmological constraints from weak lensing (WL) peak counts, which we denote as `the hierarchical algorithm'. The idea of this method is to combine information from WL maps sequentially smoothed with a…