Zobrazeno 1 - 10
of 334
pro vyhledávání: '"Lasserre, Jean Bernard"'
Autor:
Lasserre, Jean-Bernard, Slot, Lucas
Christoffel polynomials are classical tools from approximation theory. They can be used to estimate the (compact) support of a measure $\mu$ on $\mathbb{R}^d$ based on its low-degree moments. Recently, they have been applied to problems in data scien
Externí odkaz:
http://arxiv.org/abs/2409.15965
We introduce a variant of the D-optimal design of experiments problem with a more general information matrix that takes into account the representation of the design space S. The main motivation is that if S $\subset$ R d is the unit ball, the unit b
Externí odkaz:
http://arxiv.org/abs/2409.04058
We introduce an infinite-dimensional version of the Christoffel function, where now (i) its argument lies in a Hilbert space of functions, and (ii) its associated underlying measure is supported on a compact subset of the Hilbert space. We show that
Externí odkaz:
http://arxiv.org/abs/2407.02019
Autor:
Dressler, Mareike, Foucart, Simon, Joldes, Mioara, de Klerk, Etienne, Lasserre, Jean-Bernard, Xu, Yuan
We consider a new multivariate generalization of the classical monic (univariate) Chebyshev polynomial that minimizes the uniform norm on the interval $[-1,1]$. Let $\Pi^*_n$ be the subset of polynomials of degree at most $n$ in $d$ variables, whose
Externí odkaz:
http://arxiv.org/abs/2405.19219
This paper explores methods for verifying the properties of Binary Neural Networks (BNNs), focusing on robustness against adversarial attacks. Despite their lower computational and memory needs, BNNs, like their full-precision counterparts, are also
Externí odkaz:
http://arxiv.org/abs/2405.17049
Autor:
Dressler, Mareike, Foucart, Simon, Joldes, Mioara, de Klerk, Etienne, Lasserre, Jean Bernard, Xu, Yuan
This article is concerned with an extension of univariate Chebyshev polynomials of the first kind to the multivariate setting, where one chases best approximants to specific monomials by polynomials of lower degree relative to the uniform norm. Explo
Externí odkaz:
http://arxiv.org/abs/2405.10438
Autor:
Lasserre, Jean-Bernard
Given a determinate (multivariate) probability measure $\mu$, we characterize Gaussian mixtures $\nu\_\phi$ which minimize the Wasserstein distance $W\_2(\mu,\nu\_\phi)$ to $\mu$ when the mixing probability measure $\phi$ on the parameters $(m,\Sigma
Externí odkaz:
http://arxiv.org/abs/2404.19378
Autor:
Lasserre, Jean-Bernard
Given two measures $\mu$, $\nu$ on Rd that satisfy Carleman's condition, we provide a numerical scheme to approximate as closely as desired the total variation distance between $\mu$ and $\nu$. It consists of solving a sequence (hierarchy) of convex
Externí odkaz:
http://arxiv.org/abs/2401.01086
Set-membership estimation (SME) outputs a set estimator that guarantees to cover the groundtruth. Such sets are, however, defined by (many) abstract (and potentially nonconvex) constraints and therefore difficult to manipulate. We present tractable a
Externí odkaz:
http://arxiv.org/abs/2311.15962
Autor:
Lasserre, Jean-Bernard, Xu, Yuan
We extend the polynomial Pell's equation satisfied by univariate Chebyshev polynomials on [--1, 1] from one variable to several variables, using orthogonal polynomials on regular domains that include cubes, balls, and simplexes of arbitrary dimension
Externí odkaz:
http://arxiv.org/abs/2307.10668