Work

Dimension-Free Estimators of Gradients of Functions with(out) Non-Independent Variables

Year: 2025

Type: article

Abstract: This study proposes a unified stochastic framework for approximating and computing the gradient of every smooth function evaluated at non-independent variables, using ℓp-spherical distributions on Rd with d,p≥1. The upper-bounds of the bias of the gradient surrogates do not suffer from the curse of dimensionality for any p≥1. Additionally, the mean squared errors (MSEs) of the gradient estimators are bounded by K0N−1d for any p∈[1,2], and by K1N−1d2/p when 2≤p≪d with N the sample size and K0,K1 some constants. Taking max2,log(d)

Source: Axioms

DOI: 10.3390/axioms15010022

Author: Matieyendou Lamboni

Institutions: Université de Montpellier, University of French Guiana, Institut de Recherche pour le Développement, UMR Espace-Dev

Language: English

Topic: Mathematical Approximation and Integration

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

OpenAlex ID: W7117488762

FWCI: 3.123

Cites: 26

Cited by: 3

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