Entropy and Sampling Numbers of Classes of Ridge Functions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10315053" target="_blank" >RIV/00216208:11320/15:10315053 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00365-014-9267-x" target="_blank" >http://dx.doi.org/10.1007/s00365-014-9267-x</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00365-014-9267-x" target="_blank" >10.1007/s00365-014-9267-x</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Entropy and Sampling Numbers of Classes of Ridge Functions

Popis výsledku v původním jazyce

We study the properties of ridge functions in high dimensions from the viewpoint of approximation theory. The function classes considered consist of ridge functions such that the profile is a member of a univariate Lipschitz class with smoothness (including infinite smoothness) and the ridge direction has -norm . First, we investigate entropy numbers in order to quantify the compactness of these ridge function classes in . We show that they are essentially as compact as the class of univariate Lipschitzfunctions. Second, we examine sampling numbers and consider two extreme cases. In the case , sampling ridge functions on the Euclidean unit ball suffers from the curse of dimensionality. Moreover, it is as difficult as sampling general multivariate Lipschitz functions, which is in sharp contrast to the result on entropy numbers. When we additionally assume that all feasible profiles have a first derivative uniformly bounded away from zero at the origin, the complexity of sampling ridge

Název v anglickém jazyce

Entropy and Sampling Numbers of Classes of Ridge Functions

Popis výsledku anglicky

We study the properties of ridge functions in high dimensions from the viewpoint of approximation theory. The function classes considered consist of ridge functions such that the profile is a member of a univariate Lipschitz class with smoothness (including infinite smoothness) and the ridge direction has -norm . First, we investigate entropy numbers in order to quantify the compactness of these ridge function classes in . We show that they are essentially as compact as the class of univariate Lipschitzfunctions. Second, we examine sampling numbers and consider two extreme cases. In the case , sampling ridge functions on the Euclidean unit ball suffers from the curse of dimensionality. Moreover, it is as difficult as sampling general multivariate Lipschitz functions, which is in sharp contrast to the result on entropy numbers. When we additionally assume that all feasible profiles have a first derivative uniformly bounded away from zero at the origin, the complexity of sampling ridge

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/LL1203" target="_blank" >LL1203: Vlastnosti funkcí a zobrazení v Sobolevových prostorech</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Constructive Approximation

ISSN

0176-4276

e-ISSN

—

Svazek periodika

42

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

34

Strana od-do

231-264

Kód UT WoS článku

000360669800003

EID výsledku v databázi Scopus

2-s2.0-84940786563