Related papers: Fully Bayesian Unfolding with Regularization

Unfolding, in the context of high-energy particle physics, refers to the process of removing detector distortions in experimental data. The resulting unfolded measurements are straightforward to use for direct comparisons between…

Regularisation allows one to handle ill-posed inverse problems. Here we focus on discrete unfolding problems. The properties of the results are characterised by the consistency between measurements and unfolding result and by the posterior…

Normalizing flows have emerged as an important family of deep neural networks for modelling complex probability distributions. In this note, we revisit their coupling and autoregressive transformation layers as probabilistic graphical…

1. Parameter inference from distorted measurements is discussed. 2. Smeared measurements are unfolded without explicit regularization. The corresponding results are unbiased and permit to fit parameters and to apply quantitative…

The usual nonparametric approach to spectral analysis is revisited within the regularization framework. Both usual and windowed periodograms are obtained as the squared modulus of the minimizer of regularized least squares criteria. Then,…

Unfolding in high energy physics represents the correction of measured spectra in data for the finite detector efficiency, acceptance, and resolution from the detector to particle level. Recent machine learning approaches provide unfolding…

During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…

This paper describes the treatment of systematic uncertainties in a Likelihood formalism. RooUnfold, which includes most of the unfolding methods that are commonly used in particle physics, is used to compare a newly implemented method…

Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP…

We develop variational regularization methods which leverage sparsity-promoting priors to solve severely ill posed inverse problems defined on the 3D ball (i.e. the solid sphere). Our method solves the problem natively on the ball and thus…

A Bayesian method application to the deconvolution of EXAFS spectra is considered. It is shown that for purposes of EXAFS spectroscopy, from the infinitely large number of Bayesian solutions it is possible to determine an optimal range of…

The high energy physics unfolding problem is an important statistical inverse problem in data analysis at the Large Hadron Collider (LHC) at CERN. The goal of unfolding is to make nonparametric inferences about a particle spectrum from…

Hyperspectral analysis has gained popularity over recent years as a way to infer what materials are displayed on a picture whose pixels consist of a mixture of spectral signatures. Computing both signatures and mixture coefficients is known…

Bayesian clustering methods have the widely touted advantage of providing a probabilistic characterization of uncertainty in clustering through the posterior distribution. An amazing variety of priors and likelihoods have been proposed for…

Bayesian inference allows expressing the uncertainty of posterior belief under a probabilistic model given prior information and the likelihood of the evidence. Predominantly, the likelihood function is only implicitly established by a…

In the problem of spotlight mode airborne synthetic aperture radar (SAR) image formation, it is well-known that data collected over a wide azimuthal angle violate the isotropic scattering property typically assumed. Many techniques have…

We develop a weighted Bayesian Bootstrap (WBB) for machine learning and statistics. WBB provides uncertainty quantification by sampling from a high dimensional posterior distribution. WBB is computationally fast and scalable using only…

Parameter-space regularization in neural network optimization is a fundamental tool for improving generalization. However, standard parameter-space regularization methods make it challenging to encode explicit preferences about desired…

While several previous studies have devised methods for segmentation of polyps, most of these methods are not rigorously assessed on multi-center datasets. Variability due to appearance of polyps from one center to another, difference in…

Beamforming is an essential step in the ultrasound image formation pipeline and has recently attracted growing interest. An important goal of beamforming is to increase the image spatial resolution, or in other words to narrow down the…