Concept

Nonlinear dimensionality reduction

Publications associées (497)

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Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...

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Mapping Bibliotheca Hertziana

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The project introduces an innovative visual method for analysing libraries and archives, with a focus on Bibliotheca Hertziana’s library collection. This collection, which dates back over a century, is examined by integrating user loan data with deep mappi ...

2024

Relaxing the Additivity Constraints in Decentralized No-Regret High-Dimensional Bayesian Optimization

Patrick Thiran

Bayesian Optimization (BO) is typically used to optimize an unknown function f that is noisy and costly to evaluate, by exploiting an acquisition function that must be maximized at each optimization step. Even if provably asymptotically optimal BO algorith ...

2024

High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularization

Volkan Cevher, Fanghui Liu

This paper studies kernel ridge regression in high dimensions under covariate shifts and analyzes the role of importance re-weighting. We first derive the asymptotic expansion of high dimensional kernels under covariate shifts. By a bias-variance decomposi ...

2024

Towards Trustworthy Deep Learning for Image Reconstruction

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The remarkable ability of deep learning (DL) models to approximate high-dimensional functions from samples has sparked a revolution across numerous scientific and industrial domains that cannot be overemphasized. In sensitive applications, the good perform ...

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Randomized low-rank approximation and its applications

Ulf David Persson

In this thesis we will present and analyze randomized algorithms for numerical linear algebra problems. An important theme in this thesis is randomized low-rank approximation. In particular, we will study randomized low-rank approximation of matrix functio ...

EPFL2024

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Simone Deparis, Riccardo Tenderini, Nicholas Mueller

In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

Philadelphia2024

Randomized flexible GMRES with deflated restarting

Laura Grigori, Emeric Martin

For a high dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in computational costs as well as numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g. to the generaliz ...

Springer2024

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

Jan Sickmann Hesthaven, Federico Pichi

The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real -time and many-query evaluations of parametric ...

San Diego2024

Portfolio Construction with Hierarchical Momentum

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This article presents a portfolio construction approach that combines the hierarchical clustering of a large asset universe with the stock price momentum. On one hand, investing in high-momentum stocks enhances returns by capturing the momentum premium. On ...

Pageant Media Ltd2024

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