Publications associées à Théorème de Taylor

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

Higher Order Asymptotics: Applications to Satellite Conjunction and Boundary Problems

Soumaya Elkantassi

Higher-order asymptotics provide accurate approximations for use in parametric statistical modelling. In this thesis, we investigate using higher-order approximations in two-specific settings, with a particular emphasis on the tangent exponential model. ...

EPFL2023

Differential Entropy of the Conditional Expectation Under Additive Gaussian Noise

Michael Christoph Gastpar, Alper Köse, Ahmet Arda Atalik

The conditional mean is a fundamental and important quantity whose applications include the theories of estimation and rate-distortion. It is also notoriously difficult to work with. This paper establishes novel bounds on the differential entropy of the co ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

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 lognormal 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 solut ...

2020

Support and approximation properties of Hermite splines

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

In this paper, we formally investigate two mathematical aspects of Hermite splines that are relevant to practical applications. We first demonstrate that Hermite splines are maximally localized, in the sense that the size of their support is minimal among ...

2020

Functional penalised basis pursuit on spheres

Matthieu Martin Jean-André Simeoni

In this work, we propose a unified theoretical and practical spherical approximation framework for functional inverse problems on the hypersphere. More specifically, we consider recovering spherical fields directly in the continuous domain using functional ...

2020

Functional Inverse Problems on Spheres: Theory, Algorithms and Applications

Matthieu Martin Jean-André Simeoni

Many scientific inquiries in natural sciences involve approximating a spherical field -namely a scalar quantity defined over a continuum of directions- from generalised samples of the latter (e.g. directional samples, local averages, etc). Such an approxim ...

EPFL2020

Convergence analysis of Padé approximations for Helmholtz frequency response problems

Fabio Nobile, Francesca Bonizzoni

The present work concerns the approximation of the solution map

S

associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution ...

2018

Secure numerical and logical multi party operations

Bin Lu

We derive algorithms for efficient secure numerical and logical operations in the semi-honest model ensuring statistical or perfect security for secure multi-party computation (MPC). To derive our algorithms for trigonometric functions, we use basic mathem ...

Elsevier Science Bv2017

An Analytical Model for Beam Flexure Modules Based on Timoshenko Beam Theory

Simon Nessim Henein, Mohammad Hussein Kahrobaiyan, Mohamed Gamal Abdelrahman Ahmed Zanaty

Short beams are the key building blocks in many compliant mechanisms. Hence, deriving a simple yet accurate model of their elastokinematics is an important issue. Since the Euler-Bernoulli beam theory fails to accurately model these beams, we use the Timos ...

2017

A Modulated-Gradient Parametrization for the Large-Eddy Simulation of the Atmospheric Boundary Layer Using the Weather Research and Forecasting Model

Fernando Porté Agel, Sina Khani

The performance of the modulated-gradient subgrid-scale (SGS) model is investigated using large-eddy simulation (LES) of the neutral atmospheric boundary layer within the weather research and forecasting model. Since the model includes a finite-difference ...

Springer2017

Tensor train approximation of moment equations for elliptic equations with lognormal coefficient

Fabio Nobile, Daniel Kressner, Francesca Bonizzoni

We study an elliptic equation with stochastic coefficient modeled as a lognormal random field. A perturbation approach is adopted, expanding the solution in Taylor series around the nominal value of the coefficient. The resulting recursive deterministic pr ...

Elsevier2016

Dimensionality Reduction in Dynamic Optimization under Uncertainty

Napat Rujeerapaiboon

Dynamic optimization problems affected by uncertainty are ubiquitous in many application domains. Decision makers typically model the uncertainty through random variables governed by a probability distribution. If the distribution is precisely known, then ...

EPFL2016

Bilinear Generalized Approximate Message Passing—Part I: Derivation

Volkan Cevher

In this paper, we extend the generalized approximate message passing (G-AMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of compressive sensing, to the generalized-bilinear case, which enables its applica ...

Institute of Electrical and Electronics Engineers2014

Perturbation analysis for the Darcy problem with log-normal permeability

Fabio Nobile, Francesca Bonizzoni

We study the single-phase flow in a saturated, bounded heterogeneous porous medium. We model the permeability as a log-normal random field. We perform a perturbation analysis, expanding the solution in Taylor series. The series is directly computable in th ...

2014

Aggressively Truncated Taylor Series Method For Accurate Computation Of Exponentials Of Essentially Nonnegative Matrices

Meiyue Shao

Small relative perturbations to the entries of an essentially nonnegative matrix introduce small relative errors to entries of its exponential. It is thus desirable to compute the exponential with high componentwise relative accuracy. Taylor series approxi ...

Siam Publications2014

FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data

Michaël Unser, Suliana Manley, Cédric René Jean Vonesch, Hagay Kirshner, Seamus John Holden, Lina Carlini

Super resolution microscopy such as STORM and (F) PALM is now a well known method for biological studies at the nanometer scale. However, conventional imaging schemes based on sparse activation of photo-switchable fluorescent probes have inherently slow te ...

Nature Publishing Group2014

Threshold Saturation in Spatially Coupled Constraint Satisfaction Problems

Rüdiger Urbanke, Nicolas Macris, Seyed Hamed Hassani

We consider chains of random constraint satisfaction models that are spatially coupled across a finite window along the chain direction. We investigate their phase diagram at zero temperature using the survey propagation formalism and the interpolation met ...

Springer Verlag2013

Proof of a conjecture by Gazeau et al. using the Gould-Hopper polynomials

Olivier Lévêque

We provide here some probabilistic interpretations of the generalized binomial distributions proposed by Gazeau et al. ["Generating functions for generalized binomial distributions," J. Math. Phys. 53, 103304 (2012)]. In the second part, we prove the "stro ...

Amer Inst Physics2013

A modulated gradient model for scalar transport in large-eddy simulation of the atmospheric boundary layer

Fernando Porté Agel, Hao Lu

As a simple alternative to the standard eddy-diffusivity closure, a nonlinear subgrid-scale (SGS) flux model is introduced and implemented in simulations of a neutral atmospheric boundary layer and a stable atmospheric boundary layer. The new model compute ...

American Institute of Physics2013