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Lyapunov Exponents of Random Walks in Small Random Potential: The Lower Bound

Publications associées (29)

RANDOMIZED JOINT DIAGONALIZATION OF SYMMETRIC

Given a family of nearly commuting symmetric matrices, we consider the task of computing an orthogonal matrix that nearly diagonalizes every matrix in the family. In this paper, we propose and analyze randomized joint diagonalization (RJD) for performing t ...

Siam Publications2024

Random matrix methods for high-dimensional machine learning models

Antoine Philippe Michel Bodin

In the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...

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

Information Spectrum Converse for Minimum Entropy Couplings and Functional Representations

Yanina Yurina Shkel

Given two jointly distributed random variables (X,Y), a functional representation of X is a random variable Z independent of Y, and a deterministic function g(⋅,⋅) such that X=g(Y,Z). The problem of finding a minimum entropy functional representation is kn ...

2023

Sensitivity to user mischaracterizations in electric vehicle charging

Nils Gustav Nilsson

In this paper, we consider electric vehicle charging facilities that offer various levels of service, i.e., charging rates, for varying prices such that rational users choose a level of service that minimizes the total cost to themselves including an oppor ...

ELSEVIER2023

Resource aware pricing for electric vehicle charging

Nils Gustav Nilsson

Electric vehicle charging facilities offer their capacity constrained electric charge and parking to users for a fee. As electric vehicle adoption grows, so too does the potential for excessive resource utilization. In this paper, we study how prices set b ...

PERGAMON-ELSEVIER SCIENCE LTD2023

Regressive Tomography and Direct Regressive Reconstruction: A Research Note

Henri Weisen

Two related methods for inverting line-integrated measurements are presented in this research paper in the context of the recent deuterium-tritium experiments in the JET tokamak. Unlike traditional methods of tomography, these methods rely on making use of ...

2023

A Functional Perspective on Information Measures

Amedeo Roberto Esposito

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

EPFL2022

Preconditioners for robust optimal control problems under uncertainty

Fabio Nobile, Tommaso Vanzan

The discretization of robust quadratic optimal control problems under uncertainty using the finite element method and the stochastic collocation method leads to large saddle-point systems, which are fully coupled across the random realizations. Despite its ...

2023

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

Optimal Matching of Random Parts

Thomas Alois Weber

This paper examines the minimization of the cost for an expected random production output, given an assembly of finished goods from two random inputs, matched in two categories. We describe the optimal input portfolio, first using the standard normal appro ...

2022

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

Discrete Optimal Transport with Independent Marginals is #P-Hard

Daniel Kuhn, Soroosh Shafieezadeh Abadeh, Bahar Taskesen

We study the computational complexity of the optimal transport problem that evaluates the Wasser- stein distance between the distributions of two K-dimensional discrete random vectors. The best known algorithms for this problem run in polynomial time in th ...

2023

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

Victor Panaretos, Julien René Pierre Fageot, Matthieu Martin Jean-André Simeoni, Alessia Caponera

We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distribute ...

2022

Generalization Error Bounds Via Rényi-, f-Divergences and Maximal Leakage

Michael Christoph Gastpar, Ibrahim Issa, Amedeo Roberto Esposito

In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two random variables. ...

2021

Feedback and Common Information: Bounds and Capacity for Gaussian Networks

Erixhen Sula

Network information theory studies the communication of information in a network and considers its fundamental limits. Motivating from the extensive presence of the networks in the daily life, the thesis studies the fundamental limits of particular network ...

EPFL2021

Common Information Components Analysis

Michael Christoph Gastpar, Erixhen Sula

Wyner's common information is a measure that quantifies and assesses the commonality between two random variables. Based on this, we introduce a novel two-step procedure to construct features from data, referred to as Common Information Components Analysis ...

2021

A hybrid collocation-perturbation approach for PDEs with random domains

Fabio Nobile

Consider a linear elliptic PDE defined over a stochastic stochastic geometry a function of N random variables. In many application, quantify the uncertainty propagated to a quantity of interest (QoI) is an important problem. The random domain is split into ...

2021

On Randomized Trace Estimates for Indefinite Matrices with an Application to Determinants

Daniel Kressner, Alice Cortinovis

Randomized trace estimation is a popular and well-studied technique that approximates the trace of a large-scale matrix B by computing the average of x(T) Bx for many samples of a random vector X. Often, B is symmetric positive definite (SPD) but a number ...

2022

Distributional Robustness in Mechanism Design

Cagil Kocyigit

Mechanism design theory examines the design of allocation mechanisms or incentive systems involving multiple rational but self-interested agents and plays a central role in many societally important problems in economics. In mechanism design problems, agen ...

EPFL2020