Publications associées à Random field

Positive Definite Completions and Continuous Graphical Models

This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...

EPFL2023

Intrinsic area near the origin for self-similar growth-fragmentations and related random surfaces

François Gaston Ged

We study the behaviour of a natural measure defined on the leaves of the genealogical tree of some branching processes, namely self-similar growth-fragmentation processes. Each particle, or cell, is attributed a positive mass that evolves in continuous tim ...

2022

Using wavelets to capture deviations from smoothness in galaxy-scale strong lenses

Frédéric Courbin, Aymeric Alexandre Galan, Georgios Vernardos, Austin Chandler Peel

Modeling the mass distribution of galaxy-scale strong gravitational lenses is a task of increasing difficulty. The high-resolution and depth of imaging data now available render simple analytical forms ineffective at capturing lens structures spanning a la ...

EDP SCIENCES S A2022

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

Certified And Fast Computations With Shallow Covariance Kernels

Daniel Kressner, Stefano Massei

Many techniques for data science and uncertainty quantification demand efficient tools to handle Gaussian random fields, which are defined in terms of their mean functions and covariance operators. Recently, parameterized Gaussian random fields have gained ...

AMER INST MATHEMATICAL SCIENCES-AIMS2020

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

Optimal errors and phase transitions in high-dimensional generalized linear models

Nicolas Macris, Jean François Emmanuel Barbier, Florent Gérard Krzakala, Lenka Zdeborová

Generalized linear models (GLMs) are used in high-dimensional machine learning, statistics, communications, and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing, error-corre ...

National Academy of Sciences2019

Variational Methods for Human Modeling

Timur Bagautdinov

A large part of computer vision research is devoted to building models and algorithms aimed at understanding human appearance and behaviour from images and videos. Ultimately, we want to build automated systems that are at least as capable as people when i ...

EPFL2018

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

Principled Parallel Mean-Field Inference for Discrete Random Fields

Pascal Fua, François Fleuret, Pierre Bruno Baqué, Timur Bagautdinov

Mean-field variational inference is one of the most popular approaches to inference in discrete random fields. Standard mean-field optimization is based on coordinate descent and in many situations can be impractical. Thus, in practice, various parallel te ...

2016