Publications related to Asymptotic expansion

The time-domain Cartesian multipole expansion of electromagnetic fields

Farhad Rachidi-Haeri, Marcos Rubinstein, Elias Per Joachim Le Boudec, Nicolas Mora Parra, Chaouki Kasmi, Emanuela Radici

Time-domain solutions of Maxwell’s equations in homogeneous and isotropic media are paramount to studying transient or broadband phenomena. However, analytical solutions are generally unavailable for practical applications, while numerical solutions are co ...

Nature Publishing Group2024

Extensions of Peer Prediction Incentive Mechanisms

Adam Julian Richardson

As large, data-driven artificial intelligence models become ubiquitous, guaranteeing high data quality is imperative for constructing models. Crowdsourcing, community sensing, and data filtering have long been the standard approaches to guaranteeing or imp ...

EPFL2024

Stability of a liquid layer draining around a horizontal cylinder: Interplay of capillary and gravity forces

François Gallaire, Shahab Eghbali, Simeon Vladimirov Djambov

We study the drainage of a viscous liquid film coating the outside of a solid horizontal cylinder, where gravity acts vertically. We focus on the limit of large Ohnesorge numbers Oh, where inertia is negligible compared to viscous effects. We first study t ...

Amer Physical Soc2024

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

Learning curves for the multi-class teacher-student perceptron

Lenka Zdeborová, Bruno Loureiro, Elisabetta Cornacchia, Bruno Loureiro, Francesca Mignacco

One of the most classical results in high-dimensional learning theory provides a closed-form expression for the generalisation error of binary classification with a single-layer teacher-student perceptron on i.i.d. Gaussian inputs. Both Bayes-optimal (BO) ...

IOP Publishing Ltd2023

Detecting whether a stochastic process is finitely expressed in a basis

Victor Panaretos, Neda Mohammadi Jouzdani

Is it possible to detect if the sample paths of a stochastic process almost surely admit a finite expansion with respect to some/any basis? The determination is to be made on the basis of a finite collection of discretely/noisily observed sample paths. We ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2023

Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective

Victor Panaretos, Neda Mohammadi Jouzdani

We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} a ...

Elsevier2024

Bayes-optimal Learning of Deep Random Networks of Extensive-width

Florent Gérard Krzakala, Lenka Zdeborová, Hugo Chao Cui

We consider the problem of learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights. We consider the asymptotic limit where the number of samples, the input dimension and the network width ...

2023

Safety in Numbers: Asymptotic Analysis of a Monitoring Problem

Emre Telatar, Reka Inovan

In this work, we introduce a setup where a monitoring entity attempts to distinguish a cheating player among a group of regular players where all players behave in order to maximize their reward. We assume that the cheating player has an "information advan ...

IEEE2022

Differential Entropy of the Conditional Expectation Under Additive Gaussian Noise

Michael Christoph Gastpar, Alper Köse, Ahmet Arda Atalik

The conditional mean is a fundamental and important quantity whose applications include the theories of estimation and rate-distortion. It is also notoriously difficult to work with. This paper establishes novel bounds on the differential entropy of the co ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Asymptotic Errors for Teacher-Student Convex Generalized Linear Models (Or: How to Prove Kabashima’s Replica Formula)

Florent Gérard Krzakala, Alia Abbara

There has been a recent surge of interest in the study of asymptotic reconstruction performance in various cases of generalized linear estimation problems in the teacher-student setting, especially for the case of i.i.d standard normal matrices. Here, we g ...

2022

Optimal denoising of rotationally invariant rectangular matrices

Florent Gérard Krzakala, Lenka Zdeborová, 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

Two-dimensional Hubbard model at finite temperature: Weak, strong, and long correlation regimes

Riccardo Rossi

We investigate the momentum-resolved spin and charge susceptibilities, as well as the chemical potential and double occupancy in the two-dimensional Hubbard model as functions of doping, temperature, and interaction strength. Through these quantities, we i ...

AMER PHYSICAL SOC2022

Exploiting Marginal Stability in Slow-Fast Quasilinear Dynamical Systems

Alessia Ferraro

The accurate investigation of many geophysical phenomena via direct numerical simulations is computationally not possible nowadays due to the huge range of spatial and temporal scales to be resolved. Therefore advances in this field rely on the development ...

EPFL2022

Unraveling looping efficiency of stochastic Cosserat polymers

Raushan Singh, Giulio Corazza

Understanding looping probabilities, including the particular case of ring closure or cyclization, of fluctuating polymers (e.g., DNA) is important in many applications in molecular biology and chemistry. In a continuum limit the configuration of a polymer ...

AMER PHYSICAL SOC2022

Parametric Estimation For Functional Autoregressive Processes On The Sphere

Alessia Caponera

The aim of this paper is to define a nonlinear least squares estimator for the spectral parameters of a spherical autoregressive process of order 1 in a parametric setting. Furthermore, we investigate on its asymptotic properties, such as weak consistency ...

2022

From coating flow patterns to porous body wake dynamics via multiscale models

Pier Giuseppe Ledda

Multiscale phenomena are involved in countless problems in fluid mechanics. Coating flows are known to exhibit a broad variety of patterns, such as wine tears in a glass and dripping of fresh paint applied on a wall. Coating flows are typically modeled und ...

EPFL2022

Aux portes du monde miroir

Frédéric Kaplan, Isabella Di Lenardo

The Mirror World is no longer an imaginary device, a mirage in a distant future, it is a reality under construction. In Europe, Asia and on the American continent, large companies and the best universities are working to build the infrastructures, to defin ...

2021

Learning, compression, and leakage: Minimising classification error via meta-universal compression principles

Michael Christoph Gastpar, Fernando Rosas de Andraca

Learning and compression are driven by the common aim of identifying and exploiting statistical regularities in data, which opens the door for fertile collaboration between these areas. A promising group of compression techniques for learning scenarios is ...

IEEE2021

Optimal Adversarial Policies in the Multiplicative Learning System With a Malicious Expert

Negar Kiyavash, Seyed Jalal Etesami

We consider a learning system based on the conventional multiplicative weight ( MW) rule that combines experts' advice to predict a sequence of true outcomes. It is assumed that one of the experts is malicious and aims to impose the maximum loss on the sys ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021