Publications related to Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem

TIC-TAC: A Framework for Improved Covariance Estimation in Deep Heteroscedastic Regression

Mathieu Salzmann, Alexandre Massoud Alahi, Megh Hiren Shukla

Deep heteroscedastic regression involves jointly optimizing the mean and covariance of the predicted distribution using the negative log-likelihood. However, recent works show that this may result in sub-optimal convergence due to the challenges associated ...

2024

The inductive bias of deep learning: Connecting weights and functions

Guillermo Ortiz Jimenez

Years of a fierce competition have naturally selected the fittest deep learning algorithms. Yet, although these models work well in practice, we still lack a proper characterization of why they do so. This poses serious questions about the robustness, trus ...

EPFL2023

Understanding Deep Neural Function Approximation in Reinforcement Learning via ϵ-Greedy Exploration

Volkan Cevher, Fanghui Liu, Luca Viano

This paper provides a theoretical study of deep neural function approximation in reinforcement learning (RL) with the ϵ-greedy exploration under the online setting. This problem setting is motivated by the successful deep Q-networks (DQN) framework that fa ...

2022

Localization errors of the stochastic heat equation

David Jean-Michel Candil

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

EPFL2022

A Structured Dictionary Perspective on Implicit Neural Representations

Pascal Frossard, Guillermo Ortiz Jimenez, Gizem Yüce, Beril Besbinar

Implicit neural representations (INRs) have recently emerged as a promising alternative to classical discretized representations of signals. Nevertheless, despite their practical success, we still do not understand how INRs represent signals. We propose a ...

IEEE COMPUTER SOC2022

Convex optimization in sums of Banach spaces

Michaël Unser, Shayan Aziznejad

We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a finite sum of compo ...

2021

MATHICSE Technical Report : Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem

Fabio Nobile, Francesca Bonizzoni

We study the Darcy boundary value problem with log-normal permeability field. We adopt a perturbation approach, expanding the solution in Taylor series around the nominal value of the coefficient, and approximating the expected value of the stochastic solu ...

MATHICSE2020

Dictionary Learning for Two-Dimensional Kendall Shapes

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann, Anna You-Lai Song

We propose a novel sparse dictionary learning method for planar shapes in the sense of Kendall, namely configurations of landmarks in the plane considered up to similitudes. Our shape dictionary method provides a good trade-off between algorithmic simplici ...

SIAM PUBLICATIONS2020

Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications

Florian Karl Richter

We obtain new results pertaining to convergence and recurrence of multiple ergodic averages along functions from a Hardy field. Among other things, we confirm some of the conjectures posed by Frantzikinakis in [Fra10; Fra16] and obtain combinatorial applic ...

2020

Single and multiple recurrence along non-polynomial sequences

Florian Karl Richter

We establish new recurrence and multiple recurrence results for a rather large family of non-polynomial functions which contains tempered functions and (non-polynomial) functions from a Hardy field with polynomial growth. In particular, we show that, somew ...

2020

Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem

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TIC-TAC: A Framework for Improved Covariance Estimation in Deep Heteroscedastic Regression

The inductive bias of deep learning: Connecting weights and functions

Understanding Deep Neural Function Approximation in Reinforcement Learning via ϵ-Greedy Exploration

Localization errors of the stochastic heat equation

A Structured Dictionary Perspective on Implicit Neural Representations

Convex optimization in sums of Banach spaces

MATHICSE Technical Report : Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem

Dictionary Learning for Two-Dimensional Kendall Shapes

Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications

Single and multiple recurrence along non-polynomial sequences

TIC-TAC: A Framework for Improved Covariance Estimation in Deep Heteroscedastic Regression

MATHICSE Technical Report : Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem

A Structured Dictionary Perspective on Implicit Neural Representations

The inductive bias of deep learning: Connecting weights and functions

Understanding Deep Neural Function Approximation in Reinforcement Learning via ϵ-Greedy Exploration

Localization errors of the stochastic heat equation

Convex optimization in sums of Banach spaces

Dictionary Learning for Two-Dimensional Kendall Shapes

Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications

Single and multiple recurrence along non-polynomial sequences