Réduction de la dimensionnalité

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Publications associées (30)

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Unlabeled Principal Component Analysis and Matrix Completion

Yunzhen Yao, Liangzu Peng

We introduce robust principal component analysis from a data matrix in which the entries of its columns have been corrupted by permutations, termed Unlabeled Principal Component Analysis (UPCA). Using algebraic geometry, we establish that UPCA is a well-de ...

Microtome Publishing2024

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Alfio Quarteroni, Francesco Regazzoni, Stefano Pagani

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 ...

Nature Portfolio2024

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

Robust machine learning for neuroscientific inference

Steffen Schneider

Modern neuroscience research is generating increasingly large datasets, from recording thousands of neurons over long timescales to behavioral recordings of animals spanning weeks, months, or even years. Despite a great variety in recording setups and expe ...

EPFL2024

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

Deep learning approach for identification of H II regions during reionization in 21-cm observations - II. Foreground contamination

Jean-Paul Richard Kneib, Emma Elizabeth Tolley, Tianyue Chen, Michele Bianco

The upcoming Square Kilometre Array Observatory will produce images of neutral hydrogen distribution during the epoch of reionization by observing the corresponding 21-cm signal. However, the 21-cm signal will be subject to instrumental limitations such as ...

Oxford Univ Press2024

Transportation-based functional ANOVA and PCA for covariance operators

Victor Panaretos, Yoav Zemel, Valentina Masarotto

We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Vari ...

Inst Mathematical Statistics-Ims2024

Towards Trustworthy Deep Learning for Image Reconstruction

Alexis Marie Frederic Goujon

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 ...

EPFL2024

Spectral Estimators for High-Dimensional Matrix Inference

Farzad Pourkamali

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

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Deep learning approach for identification of H II regions during reionization in 21-cm observations - II. Foreground contamination

Jean-Paul Richard Kneib, Emma Elizabeth Tolley, Tianyue Chen, Michele Bianco

Oxford Univ Press2024