Non-local Functionals Related to the Total Variation and Connections with Image Processing

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. We study very weak solutions to scalar Euler-Lagrange equations associated with quadratic convex functionals. We investigate whether W1,1 solutions are necessarily W 1,2 Nash and Schauder applicable. We answer this question positively for a suitable clas ...

Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of wh ...

Borrowing some quotes from Harper Lee's novel "To Kill A Mockingbird" to help frame our manuscript, we discuss methods to profile local proteomes. We initially focus on chemical biology regimens that function in live organisms and use reactive biotin speci ...

Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...

We propose a method for sensor array self-localization using a set of sources at unknown locations. The sources produce signals whose times of arrival are registered at the sensors. We look at the general case where neither the emission times of the source ...

We study the limit behaviour of sequences of non-convex, vectorial, random integral functionals, defined on W1,1, whose integrands are ergodic and satisfy degenerate linear growth conditions. The latter involve suitable random, scale-dependent weight-funct ...

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 ...

Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful parametric representation, the mapping between the parameter and function s ...

In this paper, we present a spatial branch and bound algorithm to tackle the continuous pricing problem, where demand is captured by an advanced discrete choice model (DCM). Advanced DCMs, like mixed logit or latent class models, are capable of modeling de ...

We present a framework for performing regression when both covariate and response are probability distributions on a compact and convex subset of

\R^d

. Our regression model is based on the theory of optimal transport and links the conditional Fr'echet m ...

The dorsomedial prefrontal cortex/dorsal anterior cingulate cortex (dmPFC/dACC) is a brain area subject to many theories and debates over its function(s). Even its precise anatomical borders are subject to much controversy. In the past decades, the dmPFC/d ...

Carbon dioxide generated by the human body and exhaled (VCO2) is commonly used for ventilation controls, while the metabolic rate (i.e., energy expenditure EE) is an important parameter defining human thermal comfort in buildings. These two parameters are ...

In this paper, we analyze the recently proposed stochastic primal-dual hybrid gradient (SPDHG) algorithm and provide new theoretical results. In particular, we prove almost sure convergence of the iterates to a solution with convexity and linear convergenc ...

We consider distributed optimization over several devices, each sending incremental model updates to a central server. This setting is considered, for instance, in federated learning. Various schemes have been designed to compress the model updates in orde ...

This work develops new algorithms with rigorous efficiency guarantees for infinite horizon imitation learning (IL) with linear function approximation without restrictive coherence assumptions. We begin with the minimax formulation of the problem and then o ...

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 ...

We obtain new Fourier interpolation and uniqueness results in all dimensions, extending methods and results by the first author and M. Sousa [11] and the second author [12]. We show that the only Schwartz function which, together with its Fourier transform ...

We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...

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 ...

We propose an adaptive variance-reduction method, called AdaSpider, for minimization of L-smooth, non-convex functions with a finite-sum structure. In essence, AdaSpider combines an AdaGrad-inspired [Duchi et al., 2011, McMahan & Streeter, 2010], but a fai ...

Non-local Functionals Related to the Total Variation and Connections with Image Processing

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WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS

Generalization of Scaled Deep ResNets in the Mean-Field Regime

Climbing into their Skin to Understand Contextual Protein-Protein Associations and Localizations: Functional Investigations in Transgenic Live Model Organisms

Augmented Lagrangian Methods for Provable and Scalable Machine Learning

Localizing Unsynchronized Sensors With Unknown Sources

Stochastic homogenization of degenerate integral functionals with linear growth

Functional data analysis with rough sample paths?

Stable parameterization of continuous and piecewise-linear functions

A Spatial Branch and Bound Algorithm for Continuous Pricing with Advanced Discrete Choice Demand Modeling

Distributional Regression and Autoregression via Optimal Transport

Debates on the dorsomedial prefrontal/dorsal anterior cingulate cortex: insights for future research

Inter- and intra-individual variability in CO2 production and metabolic rate

On The Convergence Of Stochastic Primal-Dual Hybrid Gradient

Stochastic distributed learning with gradient quantization and double-variance reduction

Proximal Point Imitation Learning

Localization errors of the stochastic heat equation

Perturbed Fourier uniqueness and interpolation results in higher dimensions

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

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

Adaptive Stochastic Variance Reduction for Non-convex Finite-Sum Minimization