Nonideal sampling and regularized interpolation of noisy data

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Towards Trustworthy Deep Learning for Image Reconstruction

Alexis Marie Frederic Goujon

The remarkable ability of deep learning (DL) models to approximate high-dimensional functions from samples has sparked a revolution across numerous scientific and industrial domains that cannot be overemphasized. In sensitive applications, the good perform ...

EPFL2024

Gibbs sampling the posterior of neural networks

Lenka Zdeborová, Emanuele Troiani, Giovanni Piccioli

In this paper, we study sampling from a posterior derived from a neural network. We propose a new probabilistic model consisting of adding noise at every pre- and post-activation in the network, arguing that the resulting posterior can be sampled using an ...

Iop Publishing Ltd2024

A Combination Technique for Optimal Control Problems Constrained by Random PDEs

Fabio Nobile, Tommaso Vanzan

We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of optimal control problems (OCPs) constrained by random partial differential equ ...

2024

Adaptive Finite Elements with Large Aspect Ratio. Application to Aluminium Electrolysis

Paride Passelli

The goal of this work is to use anisotropic adaptive finite elements for the numerical simulation of aluminium electrolysis. The anisotropic adaptive criteria are based on a posteriori error estimates derived for simplified problems. First, we consider an ...

EPFL2024

On Speed and Advantage : Results in Information Velocity and Monitoring Problems

Reka Inovan

Information theory has allowed us to determine the fundamental limit of various communication and algorithmic problems, e.g., the channel coding problem, the compression problem, and the hypothesis testing problem. In this work, we revisit the assumptions ...

EPFL2024

Generalized Bradley-Terry Models for Score Estimation from Paired Comparisons

Julien René Fageot, Le Nguyen Hoang, Sadegh Farhadkhani, Oscar Jean Olivier Villemaud

Many applications, e.g. in content recommendation, sports, or recruitment, leverage the comparisons of alternatives to score those alternatives. The classical Bradley-Terry model and its variants have been widely used to do so. The historical model conside ...

AAAI Press2024

Extensions of Peer Prediction Incentive Mechanisms

Adam Julian Richardson

As large, data-driven artificial intelligence models become ubiquitous, guaranteeing high data quality is imperative for constructing models. Crowdsourcing, community sensing, and data filtering have long been the standard approaches to guaranteeing or imp ...

EPFL2024

Interpolation and Quantifiers in Ortholattices

Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

We study quantifiers and interpolation properties in orthologic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based pro ...

Springer International Publishing Ag2024

Interpolation and Quantifiers in Ortholattices

Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

We study quantifiers and interpolation properties in ortho- logic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based p ...

2024

A Method of Moments Estimator for Interacting Particle Systems and their Mean Field Limit

Andrea Zanoni

We study the problem of learning unknown parameters in stochastic interacting particle systems with polynomial drift, interaction, and diffusion functions from the path of one single particle in the system. Our estimator is obtained by solving a linear sys ...

Siam Publications2024

Intermediate complexity atmospheric modeling in complex terrain: is it right?

Michael Lehning, Dylan Stewart Reynolds, Michael Haugeneder

Dynamic downscaling of atmospheric forcing data to the hectometer resolution has shown increases in accuracy for landsurface models, but at great computational cost. Here we present a validation of a novel intermediate complexity atmospheric model, HICAR, ...

Frontiers Media Sa2024