Publications associées à Macroscopic stability for nonfinite range kernels

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

Functional data analysis with rough sample paths?

Victor Panaretos, Neda Mohammadi Jouzdani

Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is imposed to allow for ...

TAYLOR & FRANCIS LTD2024

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

The Completion Of Covariance Kernels

Victor Panaretos, Kartik Waghmare

We consider the problem of positive-semidefinite continuation: extending a partially specified covariance kernel from a subdomain Omega of a rectangular domain I x I to a covariance kernel on the entire domain I x I. For a broad class of domains Omega call ...

INST MATHEMATICAL STATISTICS-IMS2022

Implicit Bias of SGD for Diagonal Linear Networks: a Provable Benefit of Stochasticity

Scott William Pesme, Nicolas Henri Bernard Flammarion, Loucas Pillaud-Vivien

Understanding the implicit bias of training algorithms is of crucial importance in order to explain the success of overparametrised neural networks. In this paper, we study the dynamics of stochastic gradient descent over diagonal linear networks through i ...

2021

The Error-Feedback Framework: Better Rates for SGD with Delayed Gradients and Compressed Updates

Sai Praneeth Reddy Karimireddy, Sebastian Urban Stich

We analyze (stochastic) gradient descent (SGD) with delayed updates on smooth quasi-convex and non-convex functions and derive concise, non-asymptotic, convergence rates. We show that the rate of convergence in all cases consists of two terms: (i) a stocha ...

Microtome Publishing2020

The n-term Approximation of Periodic Generalized Levy Processes

Michaël Unser, John Paul Ward, Julien René Pierre Fageot

In this paper, we study the compressibility of random processes and fields, called generalized Levy processes, that are solutions of stochastic differential equations driven by d-dimensional periodic Levy white noises. Our results are based on the estimati ...

2020

Gaussian and sparse processes are limits of generalized Poisson processes

Michaël Unser, Virginie Sophie Uhlmann, Julien René Pierre Fageot

The theory of sparse stochastic processes offers a broad class of statistical models to study signals, far beyond the more classical class of Gaussian processes. In this framework, signals are represented as realizations of random processes that are soluti ...

2020

Dynamical mean-field theory for stochastic gradient descent in Gaussian mixture classification

Francesca Mignacco, Florent Gérard Krzakala, Lenka Zdeborová

We analyze in a closed form the learning dynamics of stochastic gradient descent (SGD) for a single layer neural network classifying a high-dimensional Gaussian mixture where each cluster is assigned one of two labels. This problem provides a prototype of ...

Curran Associates, Inc.2020

A Stochastic Conditioning Scheme for Diverse Human Motion Prediction

Mathieu Salzmann, Fatemehsadat Saleh

Human motion prediction, the task of predicting future 3D human poses given a sequence of observed ones, has been mostly treated as a deterministic problem. However, human motion is a stochastic process: Given an observed sequence of poses, multiple future ...

IEEE2020

Path properties of the solution to the stochastic heat equation with Levy noise

Robert Dalang, Thomas Marie Jean-Baptiste Humeau, Carsten Hao Ye Chong

We consider sample path properties of the solution to the stochastic heat equation, in Rd or bounded domains of Rd, driven by a Levy space-time white noise. When viewed as a stochastic process in time with values in an infinite-dimensional space, the solut ...

SPRINGER2019

The sources of sovereign risk: a calibration based on Levy stochastic processes

Sylvain Jean Pascal Carré, Daniel Cohen

Governments choose to issue risky or riskless debt depending on the nature of the stochastic process of output. We use Brownian motion and Poisson shocks a modeling method in the literature on corporate default known as Levy processes to approximate a deco ...

ELSEVIER SCIENCE BV2019

Extremal behaviour of aggregated data with an application to downscaling

Sebastian Engelke, Raphaël Gérard Théodore Michel Marie de Deloÿe et Fourcade de Fondeville

The distribution of spatially aggregated data from a stochastic process may exhibit tail behaviour different from that of its marginal distributions. For a large class of aggregating functionals we introduce the -extremal coefficient, which quantifies this ...

OXFORD UNIV PRESS2019

Scaling Limits of Solutions of Linear Stochastic Differential Equations Driven by Levy White Noises

Michaël Unser, Julien René Pierre Fageot

Consider a random process s that is a solution of the stochastic differential equation Ls = w with L a homogeneous operator and w a multidimensional Levy white noise. In this paper, we study the asymptotic effect of zooming in or zooming out of the process ...

2019

Procrustes Metrics and Optimal Transport for Covariance Operators

Valentina Masarotto

Covariance operators play a fundamental role in functional data analysis, providing the canonical means to analyse functional variation via the celebrated Karhunen-Loève expansion. These operators may themselves be subject to variation, for instance in con ...

EPFL2019

Calibration Aspects of INS Navigation

Philipp Clausen

The use of a Bayesian filter (e.g., Kalman filter) for the fusion of information from satellite positioning and inertial navigation is a common approach in many applications, where the knowledge of position, velocity, and attitude in space are of great int ...

EPFL2019

Stochastic bedload transport in mountain streams

Christophe Ancey

Describing bedload transport as a stochastic process is an idea that emerged in the 1930s with the pioneering work of Einstein. For a long time, the stochastic approach attracted marginal attention, but the situation has radically changed over the last dec ...

EDP Sciences2018

Gaussian versus Sparse Stochastic Processes : Construction, Regularity, Compressibility

Julien René Pierre Fageot

Although our work lies in the field of random processes, this thesis was originally motivated by signal processing applications, mainly the stochastic modeling of sparse signals. We develop a mathematical study of the innovation model, under which a signal ...

EPFL2017

On the Besov regularity of periodic Levy noises

Michaël Unser, John Paul Ward, Julien René Pierre Fageot

In this paper, we study the Besov regularity of Levy white noises on the d-dimensional torus. Due to their rough sample paths, the white noises that we consider are defined as generalized stochastic fields. We, initially, obtain regularity results for gene ...

Academic Press Inc Elsevier Science2017

Generalized Pickands constants and stationary max-stable processes

Sebastian Engelke

Pickands constants play a crucial role in the asymptotic theory of Gaussian processes. They are commonly defined as the limits of a sequence of expectations involving fractional Brownian motions and, as such, their exact value is often unknown. Recently, D ...

Springer Verlag2017