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pro vyhledávání: '"Lasserre, Jean"'
Autor:
Lasserre, Jean B.
Publikováno v:
Comptes Rendus. Mathématique, Vol 361, Iss G5, Pp 935-952 (2023)
We first interpret Pell’s equation satisfied by Chebyshev polynomials for each degree $t$, as a certain Positivstellensatz, which then yields for each integer $t$, what we call a generalized Pell’s equation, satisfied by reciprocals of Christoffe
Externí odkaz:
https://doaj.org/article/18ca7a2c09c34378948a07ad629a7da0
Autor:
Lasserre, Jean B.
Publikováno v:
Comptes Rendus. Mathématique, Vol 360, Iss G8, Pp 919-928 (2022)
We show that the empirical Christoffel function associated with a cloud of finitely many points sampled from a distribution, can provide a simple tool for supervised classification in data analysis, with good generalization properties.
Externí odkaz:
https://doaj.org/article/29fbb5144fc84811ba12e678dc8a55b9
Autor:
Lasserre, Jean B.
Publikováno v:
Comptes Rendus. Mathématique, Vol 360, Iss G9, Pp 1071-1079 (2022)
We show that the Christoffel function (CF) factorizes (or can be disintegrated) as the product of two Christoffel functions, one associated with the marginal and the another related to the conditional distribution, in the spirit of “the CF of the d
Externí odkaz:
https://doaj.org/article/7933d0edff4d430eb082cc42939c4e37
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