Publications related to Dictionary Identifiability from Few Training Samples

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

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

Randomized flexible GMRES with deflated restarting

Emeric Martin, Laura Grigori

For a high-dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in terms of both computational cost and numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g., to the ge ...

Springer2024

Spectral representation of EEG data using learned graphs with application to motor imagery decoding

Dimitri Nestor Alice Van De Ville, Hamid Behjat, Maliheh Miri

Electroencephalography (EEG) data entail a complex spatiotemporal structure that reflects ongoing organi-zation of brain activity. Characterization of the spatial patterns is an indispensable step in numerous EEG processing pipelines. We present a novel me ...

Elsevier Sci Ltd2023

Dynamical Low-Rank Approximation for Stochastic Differential Equations

Fabio Nobile, Yoshihito Kazashi, Fabio Zoccolan

In this paper, we set the mathematical foundations of the Dynamical Low-Rank Approximation (DLRA) method for stochastic differential equations (SDEs). DLRA aims at approximating the solution as a linear combination of a small number of basis vectors with r ...

American Mathematical Society (AMS)2024

Learned Compressive Representations for Single-Photon 3D Imaging

Claudio Bruschini, Edoardo Charbon, Andrei Ardelean, Mohit Gupta

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

Harmonic decomposition of the trace of 1D transfer matrices in layered media

Antonio Joaquin Garcia Suarez

The Transfer Matrix formalism is ubiquitous when it comes to study wave propagation in various stratified media, applications ranging from Seismology to Quantum Mechanics. A relation between variables at two points in two different layers can be establishe ...

2022

Unified theory of atom-centered representations and message-passing machine-learning schemes

Michele Ceriotti, Jigyasa Nigam, Guillaume André Jean Fraux, Sergey Pozdnyakov

Data-driven schemes that associate molecular and crystal structures with their microscopic properties share the need for a concise, effective description of the arrangement of their atomic constituents. Many types of models rely on descriptions of atom-cen ...

AIP Publishing2022

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

Statistical limits of dictionary learning: Random matrix theory and the spectral replica method

Nicolas Macris, Jean François Emmanuel Barbier

We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast with most existin ...

AMER PHYSICAL SOC2022

Optimal radial basis for density-based atomic representations

Félix Benedito Clément Musil, Michele Ceriotti, Alexander Jan Goscinski, Jigyasa Nigam, Sergey Pozdnyakov

The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular representations ...

2021

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

Compress-and-restart block Krylov subspace methods for Sylvester matrix equations

Daniel Kressner, Stefano Massei, Kathryn Dianne Lund

Block Krylov subspace methods (KSMs) comprise building blocks in many state-of-the-art solvers for large-scale matrix equations as they arise, for example, from the discretization of partial differential equations. While extended and rational block Krylov ...

2020

New Results in Integer and Lattice Programming

Christoph Hunkenschröder

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

,

b \in \Z^m

,

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

EPFL2020

Solving Rank-Structured Sylvester And Lyapunov Equations

Stefano Massei

We consider the problem of efficiently solving Sylvester and Lyapunov equations of medium and large scale, in case of rank-structured data, i.e., when the coefficient matrices and the right-hand side have low-rank off-diagonal blocks. This comprises proble ...

SIAM PUBLICATIONS2018

Fast hierarchical solvers for symmetric eigenvalue problems

Ana Susnjara

In this thesis we address the computation of a spectral decomposition for symmetric banded matrices. In light of dealing with large-scale matrices, where classical dense linear algebra routines are not applicable, it is essential to design alternative tech ...

EPFL2018

On quadratic matrix equations with infinite size coefficients encountered in QBD stochastic processes

Stefano Massei

Matrix equations of the kind A(1)X(2)+A(0)X+A(-1)=X, where both the matrix coefficients and the unknown are semi-infinite matrices belonging to a Banach algebra, are considered. These equations, where coefficients are quasi-Toeplitz matrices, are encounter ...

WILEY2018

Unified Theory for Recovery of Sparse Signals in a General Transform Domain

Kyong Hwan Jin

Compressed sensing is provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that the practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many real-world a ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2018

Ultrafast ultrasound imaging as an inverse problem: Matrix-free sparse image reconstruction

Jean-Philippe Thiran, Yves Wiaux, Dimitris Perdios, Adrien Georges Jean Besson, Rafael Eduardo Carrillo Rangel, Florian Martinez, Marcel Arditi

Conventional ultrasound (US) image reconstruction methods rely on delay-and-sum (DAS) beamforming, which is a relatively poor solution of the image reconstruction problem. An alternative to DAS consists in using iterative techniques which require both an a ...

2017

Low-rank methods for parameter-dependent eigenvalue problems and matrix equations

Petar Sirkovic

The focus of this thesis is on developing efficient algorithms for two important problems arising in model reduction, estimation of the smallest eigenvalue for a parameter-dependent Hermitian matrix and solving large-scale linear matrix equations, by extra ...

EPFL2016

Convex block-sparse linear regression with expanders - provably

Volkan Cevher, Anastasios Kyrillidis, Luca Baldassarre, Bubacarr Bah, Quoc Tran Dinh

Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of space and run-ti ...

2016