Publication

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Publications associées (31)

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

Victor Panaretos, Julien René Pierre Fageot, Matthieu Martin Jean-André Simeoni, Alessia Caponera

We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distribute ...

2022

Perturbed Fourier uniqueness and interpolation results in higher dimensions

Martin Peter Stoller, Joao Pedro Gonçalves Ramos

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 ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Covariance Estimation for Random Surfaces beyond Separability

Tomas Masák

This thesis focuses on non-parametric covariance estimation for random surfaces, i.e.~functional data on a two-dimensional domain. Non-parametric covariance estimation lies at the heart of functional data analysis, and considerations of statistical and com ...

EPFL2022

Optimal Matching of Random Parts

Thomas Alois Weber

This paper examines the minimization of the cost for an expected random production output, given an assembly of finished goods from two random inputs, matched in two categories. We describe the optimal input portfolio, first using the standard normal appro ...

2022

Quadrature-free immersed isogeometric analysis

Pablo Antolin Sanchez, Thibaut Hirschler

This paper presents a novel method for solving partial differential equations on three-dimensional CAD geometries by means of immersed isogeometric discretizations that do not require quadrature schemes. It relies on a newly developed technique for the eva ...

SPRINGER2022

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

Volkan Cevher, Ali Kavis, Leello Tadesse Dadi, Efstratios Panteleimon Skoulakis, Kimon Antonakopoulos

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 ...

2022

Strictly Real Fundamental Theorem Of Algebra Using Polynomial Interlacing

Soham Basu

Without resorting to complex numbers or any advanced topological arguments, we show that any real polynomial of degree greater than two always has a real quadratic polynomial factor, which is equivalent to the fundamental theorem of algebra. The proof uses ...

CAMBRIDGE UNIV PRESS2021

Computation of Al-Salam Carlitz and Askey-Wilson moments using Motzkin paths

Gaspard Ohlmann

In this paper we study the moments of polynomials from the Askey scheme, and we focus on Askey-Wilson polynomials. More precisely, we give a combinatorial proof for the case where d = 0. Their values have already been computed by Kim and Stanton in 2015, h ...

ELECTRONIC JOURNAL OF COMBINATORICS2021

Distributed Learning in Non-Convex Environments-Part I: Agreement at a Linear Rate

Ali H. Sayed, Stefan Vlaski

Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments. Most available wor ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Distributed Learning in Non-Convex Environments-Part II: Polynomial Escape From Saddle-Points

Ali H. Sayed, Stefan Vlaski

The diffusion strategy for distributed learning from streaming data employs local stochastic gradient updates along with exchange of iterates over neighborhoods. In Part I [3] of this work we established that agents cluster around a network centroid and pr ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

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