Integral Operator Approach to Learning Theory with Unbounded Sampling

Shao Gao Lv; Yun Long Feng

doi:10.1007/s11785-011-0139-0

Integral Operator Approach to Learning Theory with Unbounded Sampling

Shao Gao Lv
, Yun Long Feng

Mathematics and Statistics

University at Albany

City University of Hong Kong

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

This paper mainly focuses on the least square regularized regression learning algorithm in a setting of unbounded sampling. Our task is to establish learning rates by means of integral operators. By imposing a moment hypothesis on the unbounded sampling outputs and a function space condition associated with marginal distribution ρ _X, we derive learning rates which are consistent with those in the bounded sampling setting.

Original language	English
Pages (from-to)	533-548
Number of pages	16
Journal	Complex Analysis and Operator Theory
Volume	6
Issue number	3
DOIs	https://doi.org/10.1007/s11785-011-0139-0
State	Published - Jun 2012

Keywords

Capacity independent error bounds
Integral operator
Least square regularized regression
Reproducing kernel Hilbert spaces

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title = "Integral Operator Approach to Learning Theory with Unbounded Sampling",

abstract = "This paper mainly focuses on the least square regularized regression learning algorithm in a setting of unbounded sampling. Our task is to establish learning rates by means of integral operators. By imposing a moment hypothesis on the unbounded sampling outputs and a function space condition associated with marginal distribution ρ X, we derive learning rates which are consistent with those in the bounded sampling setting.",

keywords = "Capacity independent error bounds, Integral operator, Least square regularized regression, Reproducing kernel Hilbert spaces",

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AB - This paper mainly focuses on the least square regularized regression learning algorithm in a setting of unbounded sampling. Our task is to establish learning rates by means of integral operators. By imposing a moment hypothesis on the unbounded sampling outputs and a function space condition associated with marginal distribution ρ X, we derive learning rates which are consistent with those in the bounded sampling setting.

KW - Capacity independent error bounds

KW - Integral operator

KW - Least square regularized regression

KW - Reproducing kernel Hilbert spaces

UR - https://www.scopus.com/pages/publications/84863434743

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DO - 10.1007/s11785-011-0139-0

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SP - 533

EP - 548

JO - Complex Analysis and Operator Theory

JF - Complex Analysis and Operator Theory

IS - 3

ER -

Integral Operator Approach to Learning Theory with Unbounded Sampling

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Keywords

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