Publications associées à Fonction gaussienne

Spectral Estimators for High-Dimensional Matrix Inference

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

EPFL2024

Distributed Lossy Computation with Structured Codes: From Discrete to Continuous Sources

Michael Christoph Gastpar, Sung Hoon Lim, Adriano Pastore, Chen Feng

This paper considers the problem of distributed lossy compression where the goal is to recover one or more linear combinations of the sources at the decoder, subject to distortion constraints. For certain configurations, it is known that codes with algebra ...

2023

Lessons Learned from Data-Driven Building Control Experiments: Contrasting Gaussian Process-based MPC, Bilevel DeePC, and Deep Reinforcement Learning

Colin Neil Jones, Loris Di Natale, Jicheng Shi, Emilio Maddalena, Yingzhao Lian

This manuscript offers the perspective of experimentalists on a number of modern data-driven techniques: model predictive control relying on Gaussian processes, adaptive data-driven control based on behavioral theory, and deep reinforcement learning. These ...

2023

A new variable shape parameter strategy for RBF approximation using neural networks

Jan Sickmann Hesthaven

The choice of the shape parameter highly effects the behaviour of radial basis function (RBF) approximations, as it needs to be selected to balance between the ill-conditioning of the interpolation matrix and high accuracy. In this paper, we demonstrate ho ...

PERGAMON-ELSEVIER SCIENCE LTD2023

Robust discrete choice models with t-distributed kernel errors

Michel Bierlaire, Thomas Gasos, Prateek Bansal

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, ...

2023

Filter-Informed Spectral Graph Wavelet Networks for Multiscale Feature Extraction and Intelligent Fault Diagnosis

Olga Fink, Tianfu Li

Intelligent fault diagnosis has been increasingly improved with the evolution of deep learning (DL) approaches. Recently, the emerging graph neural networks (GNNs) have also been introduced in the field of fault diagnosis with the goal to make better use o ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023

Distributionally Robust Linear Quadratic Control

Daniel Kuhn, Bahar Taskesen, Cagil Kocyigit

Linear-Quadratic-Gaussian (LQG) control is a fundamental control paradigm that is studied in various fields such as engineering, computer science, economics, and neuroscience. It involves controlling a system with linear dynamics and imperfect observations ...

2023

Primordial black hole isocurvature modes from non-Gaussianity

Primordial black holes (PBHs) are black holes that might have formed in high density regions in the early universe. The presence of local-type non-Gaussianity can lead to large-scale fluctuations in the PBH formation rate. If PBHs make up a non-negligible ...

IOP Publishing Ltd2023

Machine Learning Methods for Robust Uncertainty Quantification and Controller Approximation

Emilio Maddalena

This thesis is situated at the crossroads between machine learning and control engineering. Our contributions are both theoretical, through proposing a new uncertainty quantification methodology in a kernelized context; and experimental, through investigat ...

EPFL2023

Cosmological Fisher forecasts for next-generation spectroscopic surveys

Jean-Paul Richard Kneib, Jiaxi Yu, Cheng Zhao

Next-generation spectroscopic surveys such as the MegaMapper, MUltiplexed Survey Telescope (MUST), MaunaKea Spectroscopic Explorer (MSE), and WideField Spectroscopic Telescope (WST) are foreseen to increase the number of galaxy/quasar redshifts by an order ...

OXFORD UNIV PRESS2023

The Gray-Wyner Network and Wyner's Common Information for Gaussian Sources

Michael Christoph Gastpar, Erixhen Sula

This paper presents explicit solutions for two related non-convex information extremization problems due to Gray and Wyner in the Gaussian case. The first problem is the Gray-Wyner network subject to a sum-rate constraint on the two private links. Here, ou ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Local Nondeterminism and Local Times of the Stochastic Wave Equation Driven by Fractional-Colored Noise

Cheuk Yin Lee

We investigate the existence and regularity of the local times of the solution to a linear system of stochastic wave equations driven by a Gaussian noise that is fractional in time and colored in space. Using Fourier analytic methods, we establish strong l ...

SPRINGER BIRKHAUSER2022

PoGaIN: Poisson-Gaussian Image Noise Modeling From Paired Samples

Sabine Süsstrunk, Majed El Helou, Kaan Okumus

Image noise can often be accurately fitted to a Poisson-Gaussian distribution. However, estimating the distribution parameters from a noisy image only is a challenging task. Here, we study the case when paired noisy and noise-free samples are accessible. N ...

IEEE Institute of Electrical and Electronics Engineers2022

Simultaneous Prediction of Wrist and Hand Motions via Wearable Ultrasound Sensing for Natural Control of Hand Prostheses

Xingchen Yang

Simultaneous prediction of wrist and hand motions is essential for the natural interaction with hand prostheses. In this paper, we propose a novel multi-out Gaussian process (MOGP) model and a multi-task deep learning (MTDL) algorithm to achieve simultaneo ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Phase diagram of Stochastic Gradient Descent in high-dimensional two-layer neural networks

Florent Gérard Krzakala, Lenka Zdeborová, Bruno Loureiro, Bruno Loureiro, Ludovic Théo Stephan

Despite the non-convex optimization landscape, over-parametrized shallow networks are able to achieve global convergence under gradient descent. The picture can be radically different for narrow net-works, which tend to get stuck in badly-generalizing loca ...

2022

Propagation of singularities for the stochastic wave equation

Cheuk Yin Lee

We study the existence and propagation of singularities of the solution to a one-dimensional linear stochastic wave equation driven by an additive Gaussian noise that is white in time and colored in space. Our approach is based on a simultaneous law of the ...

ELSEVIER2022

The Completion Of Covariance Kernels

Victor Panaretos, Kartik Waghmare

We consider the problem of positive-semidefinite continuation: extending a partially specified covariance kernel from a subdomain Omega of a rectangular domain I x I to a covariance kernel on the entire domain I x I. For a broad class of domains Omega call ...

INST MATHEMATICAL STATISTICS-IMS2022

Experimental demonstration of dynamic spatiotemporal structured beams that simultaneously exhibit two orbital angular momenta by combining multiple frequency lines, each carrying multiple Laguerre-Gaussian modes

Tobias Kippenberg, Maxim Karpov, Zhe Zhao, Hao Song, Xinzhou Su

In general, there are different, relatively independent forms of orbital angular momenta at a given propagation distance, which might exhibit different dynamic spatial characteristics. One type involves a beam with a helical phase-front that rotates around ...

Optica Publishing Group2022

Optimal denoising of rotationally invariant rectangular matrices

Florent Gérard Krzakala, Lenka Zdeborová, Emanuele Troiani, Vittorio Erba

In this manuscript we consider denoising of large rectangular matrices: given a noisy observation of a signal matrix, what is the best way of recovering the signal matrix itself? For Gaussian noise and rotationally-invariant signal priors, we completely ch ...

2022

Dynamical low rank approximation for uncertainty quantification of time-dependent problems

Eva Vidlicková

The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this respect, dynamical low-rank approximation (DLRA) is very a ...

EPFL2022