Publication

Hybrid regularisation and the (in)admissibility of ridge regression in infinite dimensional Hilbert spaces

Publications associées (30)

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

Michaël Unser, Pakshal Narendra Bohra, Pol del Aguila Pla

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 ...

2023

Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective

Victor Panaretos, Neda Mohammadi Jouzdani

We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} a ...

Elsevier2024

An equilibrated flux a posteriori error estimator for defeaturing problems

Ondine Gabrielle Chanon, Annalisa Buffa, Rafael Vazquez Hernandez, Denise Grappein

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 ...

2023

Near-Minimax Optimal Estimation With Shallow ReLU Neural Networks

Rahul Parhi

We study the problem of estimating an unknown function from noisy data using shallow ReLU neural networks. The estimators we study minimize the sum of squared data-fitting errors plus a regularization term proportional to the squared Euclidean norm of the ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023

(S)GD over Diagonal Linear Networks: Implicit Regularisation, Large Stepsizes and Edge of Stability

Scott William Pesme, Nicolas Henri Bernard Flammarion, Mathieu Even

In this paper, we investigate the impact of stochasticity and large stepsizes on the implicit regularisation of gradient descent (GD) and stochastic gradient descent (SGD) over diagonal linear networks. We prove the convergence of GD and SGD with macroscop ...

2023

Unbiased Likelihood Estimation of Wright–Fisher Diffusion Processes

Fabio Nobile

In this paper we propose a Monte Carlo maximum likelihood estimation strategy for discretely observed Wright–Fisher diffusions. Our approach provides an unbiased estimator of the likelihood function and is based on exact simulation techniques that are of s ...

Springer Cham2024

Regularization for distributionally robust state estimation and prediction

Jean-Sébastien Hubert Brouillon, Giancarlo Ferrari Trecate, Florian Dörfler

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 ...

2023

Stable parameterization of continuous and piecewise-linear functions

Michaël Unser, Joaquim Gonçalves Garcia Barreto Campos, Alexis Marie Frederic Goujon

Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful parametric representation, the mapping between the parameter and function s ...

2023

Reliable uncertainties: Error correlation, rotated error bars, and linear regressions in three-isotope plots and beyond

Reto Georg Trappitsch

Correlated errors of experimental data are a common but often neglected problem in physical sciences. Various tools are provided here for thorough propagation of uncertainties in cases of correlated errors. Discussed are techniques especially applicable to ...

ELSEVIER2023

Prediction of post-stroke motor recovery benefits from measures of sub-acute widespread network damages

Dimitri Nestor Alice Van De Ville, Elvira Pirondini, Maria Giulia Preti, Cyprien Alban Félicien Rivier

Rivier et al. report that global measures of brain connectivity estimated by introducing virtual lesions in healthy structural connectomes significantly increase the accuracy of motor recovery prediction in stroke patients when added to focal and clinical ...

OXFORD UNIV PRESS2023