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

Stability of Image-Reconstruction Algorithms

Michaël Unser, Pol del Aguila Pla, Sebastian Jonas Neumayer

Robustness and stability of image-reconstruction algorithms have recently come under scrutiny. Their importance to medical imaging cannot be overstated. We review the known results for the topical variational regularization strategies ( ℓ2 and ℓ1 regulariz ...

2023

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

Volkan Cevher, Luca Viano, Fanghui Liu

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

Strong Subconvexity for Self-Dual GL(3) L-Functions

Yongxiao Lin, Ramon Moreira Nunes, Zhi Qi

In this paper, we prove strong subconvexity bounds for self-dual GL(3) L-functions in the t-aspect and for GL(3) x GL(2) L-functions in the GL(2)-spectral aspect. The bounds are strong in the sense that they are the natural limit of the moment method pione ...

OXFORD UNIV PRESS2022

A Structured Dictionary Perspective on Implicit Neural Representations

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

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

Interlacing families III: Sharper restricted invertibility estimates

Adam Wade Marcus

We use the method of interlacing families of polynomials to derive a simple proof of Bourgain and Tzafriri's Restricted Invertibility Principle, and then to sharpen the result in two ways. We show that the stable rank can be replaced by the Schatten 4-norm ...

HEBREW UNIV MAGNES PRESS2022

Dictionary Learning for Two-Dimensional Kendall Shapes

Michaël Unser, Virginie Sophie Uhlmann, Julien René Pierre Fageot, 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

On long time behavior of solutions to nonlinear dispersive equations

Stefano Francesco Burzio

In part I, we address the issue of existence of solutions for Cauchy problems involving nonlinear hyperbolic equations for initial data in Sobolev spaces with scaling subcritical regularity. In particular, we analyse nonlinear estimates for null-forms in t ...

EPFL2020

Characterization of image spaces of Riemann-Liouville fractional integral operators on Sobolev spaces W-m,W-p (omega)

Jan Sickmann Hesthaven, Lijing Zhao

Fractional operators are widely used in mathematical models describing abnormal and nonlocal phenomena. Although there are extensive numerical methods for solving the corresponding model problems, theoretical analysis such as the regularity result, or the ...

SCIENCE PRESS2020

Four-dimensional drift-kinetic model for scrape-off layer plasmas

Paolo Ricci, Rogério Manuel Cabete De Jesus Jorge

A four-dimensional plasma model able to describe the scrape-off layer region of tokamak devices at arbitrary collisionality is derived in the drift-reduced limit. The basis of the model is provided by a drift-kinetic equation that retains the full nonlinea ...

2020

A deep learning framework for matching of SAR and optical imagery

Devis Tuia, Sylvain Lobry, Lloyd Haydn Hughes

SAR and optical imagery provide highly complementary information about observed scenes. A combined use of these two modalities is thus desirable in many data fusion scenarios. However, any data fusion task requires measurements to be accurately aligned. Wh ...

2020

Decompositions Of Log-Correlated Fields With Applications

Janne Matias Junnila

In this article, we establish novel decompositions of Gaussian fields taking values in suitable spaces of generalized functions, and then use these decompositions to prove results about Gaussian multiplicative chaos. We prove two decomposition theorems. Th ...

2019

Joint Sparsity with Partially Known Support and Application to Ultrasound Imaging

Jean-Philippe Thiran, Yves Wiaux, Dimitris Perdios, Adrien Georges Jean Besson

We investigate the benefits of known partial support for the recovery of joint-sparse signals and demonstrate that it is advantageous in terms of recovery performance for both rank-blind and rank-aware algorithms. We suggest extensions of several joint-spa ...

IEEE Institute of Electrical and Electronics Engineers2019

A Conditional Gradient-Based Augmented Lagrangian Framework

Volkan Cevher, Alp Yurtsever

This paper considers a generic convex minimization template with affine constraints over a compact domain, which covers key semidefinite programming applications. The existing conditional gradient methods either do not apply to our template or are too slow ...

2019

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

Sparse Dictionaries for Continuous-Domain Inverse Problems

Michaël Unser, Shayan Aziznejad, Thomas Jean Debarre

We study 1D continuous-domain inverse problems for multicomponent signals. The prior assumption on these signals is that each component is sparse in a different dictionary specified by a regularization operators. We introduce a hybrid regularization functi ...

2019

A Preconditioned Graph Diffusion LMS for Adaptive Graph Signal Processing

Ali H. Sayed, Roula Nassif

Graph filters, defined as polynomial functions of a graph-shift operator (GSO), play a key role in signal processing over graphs. In this work, we are interested in the adaptive and distributed estimation of graph filter coefficients from streaming graph s ...

IEEE COMPUTER SOC2018