Adaptive exact recovery in sparse nonparametric models

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F25%3A00639086" target="_blank" >RIV/67985807:_____/25:00639086 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s11203-025-09333-w" target="_blank" >https://doi.org/10.1007/s11203-025-09333-w</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11203-025-09333-w" target="_blank" >10.1007/s11203-025-09333-w</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Adaptive exact recovery in sparse nonparametric models

Popis výsledku v původním jazyce

We observe an unknown function of d variables f(t), t ∈ [0, 1]^d, in the Gaussian white noise model of intensity ε > 0. We assume that the function f is regular and that it is a sum of k-variate functions, where k varies from 1 to s (1 ≤ s ≤ d). These functions are unknown to us and only a few of them are nonzero. In this article, we address the problem of identifying the nonzero components of f in the case when d = d_ε → ∞ as ε → 0 and s is either fixed or s = s_ε → ∞, s = o(d) as ε → ∞. This may be viewed as a variable selection problem. We derive the conditions when exact variable selection in the model at hand is possible and provide a selection procedure that achieves this type of selection. The procedure is adaptive to a degree of model sparsity described by the sparsity parameter β ∈ (0, 1). We also derive conditions that make the exact variable selection impossible. Our results augment previous work in this area.

Název v anglickém jazyce

Adaptive exact recovery in sparse nonparametric models

Popis výsledku anglicky

We observe an unknown function of d variables f(t), t ∈ [0, 1]^d, in the Gaussian white noise model of intensity ε > 0. We assume that the function f is regular and that it is a sum of k-variate functions, where k varies from 1 to s (1 ≤ s ≤ d). These functions are unknown to us and only a few of them are nonzero. In this article, we address the problem of identifying the nonzero components of f in the case when d = d_ε → ∞ as ε → 0 and s is either fixed or s = s_ε → ∞, s = o(d) as ε → ∞. This may be viewed as a variable selection problem. We derive the conditions when exact variable selection in the model at hand is possible and provide a selection procedure that achieves this type of selection. The procedure is adaptive to a degree of model sparsity described by the sparsity parameter β ∈ (0, 1). We also derive conditions that make the exact variable selection impossible. Our results augment previous work in this area.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/EH22_008%2F0004583" target="_blank" >EH22_008/0004583: Excelentní výzkum v oblasti digitálních technologií a wellbeingu</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Statistical Inference for Stochastic Processes

ISSN

1387-0874

e-ISSN

1572-9311

Svazek periodika

28

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

26

Strana od-do

15

Kód UT WoS článku

001603299200001

EID výsledku v databázi Scopus

2-s2.0-105019810440