Robust compressive sensing of sparse signals: A review

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We prove a universality result that reduces the free energy of rank-one matrix estimation problems in the setting of mismatched prior and noise to the computation of the free energy for a modified Sherrington–Kirkpatrick spin glass. Our main result is an a ...

In inverse problems, the task is to reconstruct an unknown signal from its possibly noise-corrupted measurements. Penalized-likelihood-based estimation and Bayesian estimation are two powerful statistical paradigms for the resolution of such problems. They ...

We study the problem of learning unknown parameters in stochastic interacting particle systems with polynomial drift, interaction, and diffusion functions from the path of one single particle in the system. Our estimator is obtained by solving a linear sys ...

In the context of discrete choice modeling, the extraction of potential behavioral insights from large datasets is often limited by the poor scalability of maximum likelihood estimation. This paper proposes a simple and fast dataset-reduction method that i ...

We propose a novel approach to evaluating the ionic Seebeck coefficient in electrolytes from relatively short equilibrium molecular dynamics simulations, based on the Green-Kubo theory of linear response and Bayesian regression analysis. By exploiting the ...

In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...

Decision-making permeates every aspect of human and societal development, from individuals' daily choices to the complex decisions made by communities and institutions. Central to effective decision-making is the discipline of optimization, which seeks th ...

The p-Laplacian problem -del & sdot; ((mu + |del u|(p-2))del u) = f is considered, where mu is a given positive number. An anisotropic a posteriori residual-based error estimator is presented. The error estimator is shown to be equivalent, up to higher ord ...

The deterministic errors of an accelerometer comprise the prevailing i) bias, ii) scale factor, and iii) non-orthogonality. Together, these errors result in a nonlinear measurement model, which is conventionally solved via an iterative nonlinear least-squa ...

The increasing availability of sensing techniques provides a great opportunity for engineers to design state estimation methods, which are optimal for the system under observation and the observed noise patterns. However, these patterns often do not fulfil ...

We present a framework for performing regression when both covariate and response are probability distributions on a compact and convex subset of

\R^d

. Our regression model is based on the theory of optimal transport and links the conditional Fr'echet m ...

An a posteriori error estimator based on an equilibrated flux reconstruction is proposed for defeaturing problems in the context of finite element discretizations. Defeaturing consists in the simplification of a geometry by removing features that are consi ...

Control systems operating in real-world environments often face disturbances arising from measurement noise and model mismatch. These factors can significantly impact the perfor- mance and safety of the system. In this thesis, we aim to leverage data to de ...

Recent cosmic shear studies have shown that higher-order statistics (HOS) developed by independent teams now outperform standard two-point estimators in terms of statistical precision thanks to their sensitivity to the non-Gaussian features of large-scale ...

Outliers in discrete choice response data may result from misclassification and misreporting of the response variable and from choice behaviour that is inconsistent with modelling assumptions (e.g. random utility maximisation). In the presence of outliers, ...

We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic signals as realizati ...

We introduce Neural Network (NN for short) approximation architectures for the numerical solution of Boundary Integral Equations (BIEs for short). We exemplify the proposed NN approach for the boundary reduction of the potential problem in two spatial dime ...

Diffusion Magnetic Resonance Imaging (dMRI) is a powerful non-invasive method for studying white matter tracts of the brain. However, accurate microstructure estimation with fiber orientation distribution (FOD) using existing computational methods requires ...

Inspired by Sibson’s alpha-mutual information, we introduce a new parametric class of universal predictors. This class interpolates two well-known predictors, the mixture estimator, that includes the Laplace and the Krichevsky-Trofimov predictors, and the ...

This thesis focuses on non-parametric covariance estimation for random surfaces, i.e.~functional data on a two-dimensional domain. Non-parametric covariance estimation lies at the heart of functional data analysis, and considerations of statistical and com ...

Robust compressive sensing of sparse signals: A review

Chattez avec Graph Search

Estimating Rank-One Matrices with Mismatched Prior and Noise: Universality and Large Deviations

Statistical Inference for Inverse Problems: From Sparsity-Based Methods to Neural Networks

A Method of Moments Estimator for Interacting Particle Systems and their Mean Field Limit

Resampling estimation of discrete choice models

Seebeck Coefficient of Ionic Conductors from Bayesian Regression Analysis

Stability: a search for structure

Reliable data-driven decision-making through optimal transport

Anisotropic Adaptive Finite Elements for a p-Laplacian Problem

Linear Estimation of Deterministic Accelerometer Errors

Regularization for distributionally robust state estimation and prediction

Distributional Regression and Autoregression via Optimal Transport

An equilibrated flux a posteriori error estimator for defeaturing problems

Data-Driven Control and Optimization under Noisy and Uncertain Conditions

Euclid preparation: XXVIII. Forecasts for ten different higher-order weak lensing statistics

Robust discrete choice models with t-distributed kernel errors

A Statistical Framework to Investigate the Optimality of Signal-Reconstruction Methods

ReLU Neural Network Galerkin BEM

Robust Estimation of the Microstructure of the Early Developing Brain Using Deep Learning

Alpha-NML Universal Predictors

Covariance Estimation for Random Surfaces beyond Separability