Publications related to Basis Identification from Random Sparse Samples

Related publications (34)

Scalable kernel logistic regression with Nyström approximation: Theoretical analysis and application to discrete choice modelling

The application of kernel-based Machine Learning (ML) techniques to discrete choice modelling using large datasets often faces challenges due to memory requirements and the considerable number of parameters involved in these models. This complexity hampers ...

2025

Overcoming Distribution Shifts and Imbalance Challenges in Representation Learning for Deep Regression Models

Ismail Nejjar

Deep learning has shown remarkable potential for industrial applications, particularly in predictive maintenance and condition monitoring. A key challenge in this domain is prognostics, specifically predicting the Remaining Useful Life (RUL) of assets - a ...

EPFL2025

Generalization of Noisy SGD in Unbounded Non-convex Settings

Volkan Cevher, Leello Tadesse Dadi

We study the generalization of iterative noisy gradient schemes on smooth non-convex losses. Formally, we establish time-independent information theoretic generalization bounds for Stochastic Gradient Langevin Dynamics (SGLD) that do not diverge as the ite ...

2025

Quantifying the Unknown: Data-Driven Approaches and Applications in Energy Systems

Paul Scharnhorst

In light of the challenges posed by climate change and the goals of the Paris Agreement, electricity generation is shifting to a more renewable and decentralized pattern, while the operation of systems like buildings is increasingly electrified. This calls ...

EPFL2024

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

Asymptotics of feature learning in two-layer networks after one gradient-step

Lenka Zdeborová, Florent Gérard Krzakala, Bruno Loureiro, Hugo Chao Cui, Yatin Dandi, Luca Pesce, Yue Lu

In this manuscript, we investigate the problem of how two-layer neural networks learn features from data, and improve over the kernel regime, after being trained with a single gradient descent step. Leveraging the insight from (Ba et al., 2022), we model t ...

2024

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

The Current State of the OBI DICT Project: A Bilingual e-Dictionary of Oracle-Bone Inscriptions with AI Image Recognition

Shuo Wen

This article reports on the current state of the OBI DICT project, a bilingual e-dictionary of oracle-bone inscriptions (OBI), incorporating artificial intelligence (AI) image recognition technology. It first provides a brief overview of the development of ...

Buro Van Die Wat2024

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

Daniel Kressner, Alice Cortinovis

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

Siam Publications2024

TimeEvolver: A program for time evolution with improved error bound

Sebastian Zell

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

ELSEVIER2022

DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

Daniel Kressner, Stefano Massei, Alice Cortinovis

This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for performing low-rank up ...

SIAM PUBLICATIONS2022

Iterative refinement of Schur decompositions

Daniel Kressner, Zvonimir Bujanovic

The Schur decomposition of a square matrix A is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following task: Compute a (m ...

SPRINGER2023

Optimal denoising of rotationally invariant rectangular matrices

Lenka Zdeborová, Florent Gérard Krzakala, 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

Sparsest piecewise-linear regression of one-dimensional data

Michaël Unser, Julien René Fageot, Thomas Jean Debarre, Quentin Alain Denoyelle

We study the problem of one-dimensional regression of data points with total-variation (TV) regularization (in the sense of measures) on the second derivative, which is known to promote piecewise-linear solutions with few knots. While there are efficient a ...

Elsevier2021

Geodesic Distance on Optimally Regularized Functional Connectomes Uncovers Individual Fingerprints

Enrico Amico

Background: Functional connectomes (FCs) have been shown to provide a reproducible individual fingerprint, which has opened the possibility of personalized medicine for neuro/psychiatric disorders. Thus, developing accurate ways to compare FCs is essential ...

MARY ANN LIEBERT, INC2021

Learned Compressive Representations for Single-Photon 3D Imaging

Edoardo Charbon, Claudio Bruschini, Andrei Ardelean

Single-photon 3D cameras can record the time-of-arrival of billions of photons per second with picosecond accuracy. One common approach to summarize the photon data stream is to build a per-pixel timestamp histogram, resulting in a 3D histogram tensor that ...

Ieee Computer Soc2023

Predicting involuntary hospitalization in psychiatry: A machine learning investigation

Mehdi Gholam

Background Coercion in psychiatry is a controversial issue. Identifying its predictors and their interaction using traditional statistical methods is difficult, given the large number of variables involved. The purpose of this study was to use machine-lear ...

CAMBRIDGE UNIV PRESS2021

A Theory of Finite-Width Neural Networks: Generalization, Scaling Laws, and the Loss Landscape

Berfin Simsek

Deep learning has achieved remarkable success in various challenging tasks such as generating images from natural language or engaging in lengthy conversations with humans. The success in practice stems from the ability to successfully train massive neural ...

EPFL2023

A fast spectral divide-and-conquer method for banded matrices

Daniel Kressner, Ana Susnjara

Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3):A1325-A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix with small bandwidth, w ...

WILEY2021

Dual-frequency spectral radar retrieval of snowfall microphysics: a physics-driven deep-learning approach

Alexis Berne, Anne-Claire Marie Billault--Roux, Gionata Ghiggi

The use of meteorological radars to study snowfall microphysical properties and processes is well established, in particular via a few distinct techniques: the use of radar polarimetry, of multi-frequency radar measurements, and of the radar Doppler spectr ...

COPERNICUS GESELLSCHAFT MBH2023