相关论文: Sparsity and the Bayesian Perspective

The statistical properties of the temperature anisotropies and polarization of the of cosmic microwave background (CMB) radiation offer a powerful probe of the physics of the early universe. In recent works a statistical procedure based…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…

We consider a Bayesian framework for estimating a high-dimensional sparse precision matrix, in which adaptive shrinkage and sparsity are induced by a mixture of Laplace priors. Besides discussing our formulation from the Bayesian…

We show that the Cosmic Microwave Background (CMB) lensing trispectrum is sensitive to parity violation in Large-Scale Structure (LSS). We obtain a compact expression for the reduced lensing trispectrum that is general for any input matter…

Penalized regression methods, such as $L_1$ regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is…

Bayesian inference paradigms are regarded as powerful tools for solution of inverse problems. However, when applied to inverse problems in physical sciences, Bayesian formulations suffer from a number of inconsistencies that are often…

It is argued that the Calibrated Bayesian (CB) approach to statistical inference capitalizes on the strength of Bayesian and frequentist approaches to statistical inference. In the CB approach, inferences under a particular model are…

We investigate the impact of point spread function (PSF) fitting errors on cosmic shear measurements using the concepts of complexity and sparsity. Complexity, introduced in a previous paper, characterizes the number of degrees of freedom…

Constrained learning is prevalent in many statistical tasks. Recent work proposes distance-to-set penalties to derive estimators under general constraints that can be specified as sets, but focuses on obtaining point estimates that do not…

High-dimensional data has become ubiquitous across the sciences but presents computational and statistical challenges. A common approach to addressing these challenges is through sparsity. In this paper, we introduce a new concept of…

In high-dimensional settings, sparse structures are critical for efficiency in term of memory and computation complexity. For a linear system, to find the sparsest solution provided with an over-complete dictionary of features directly is…

This work considers methods for imposing sparsity in Bayesian regression with applications in nonlinear system identification. We first review automatic relevance determination (ARD) and analytically demonstrate the need to additional…

The widespread adoption of deep learning models in computer vision has intensified concerns about interpretability. Despite strong performance, these models are often treated as black boxes, with limited systematic investigation of their…

A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…

Weak lensing of galaxies by large scale structure can potentially measure cosmological quantities as accurately as the cosmic microwave background (CMB). However, the relation between observables and fundamental parameters is more complex…

Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumption that the unknown solution has a sparse representation…

We develop the first algorithm able to jointly compute the maximum {\it a posteriori} estimate of the Cosmic Microwave Background (CMB) temperature and polarization fields, the gravitational potential by which they are lensed, and…

Weak gravitational lensing by the intervening large-scale structure (LSS) of the Universe is the leading non-linear effect on the anisotropies of the cosmic microwave background (CMB). The integrated line-of-sight mass that causes the…

Modern statistical learning algorithms are capable of amazing flexibility, but struggle with interpretability. One possible solution is sparsity: making inference such that many of the parameters are estimated as being identically 0, which…

Recent analyses combining cosmic microwave background (CMB) and baryon acoustic oscillation (BAO) challenge particle physics constraints on the total neutrino mass, pointing to values smaller than the lower limit from neutrino oscillation…