Analysis of regularized least squares for functional linear regression model

Hongzhi Tong; Kwok Po NG

doi:10.1016/j.jco.2018.08.001

Analysis of regularized least squares for functional linear regression model

Hongzhi Tong, Kwok Po NG^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

25 Citations (Scopus)

Abstract

In this paper, we study and analyze the regularized least squares for functional linear regression model. The approach is to use the reproducing kernel Hilbert space framework and the integral operators. We show with a more general and realistic assumption on the reproducing kernel and input data statistics that the rate of excess prediction risk by the regularized least squares is minimax optimal.

Original language	English
Pages (from-to)	85-94
Number of pages	10
Journal	Journal of Complexity
Volume	49
DOIs	https://doi.org/10.1016/j.jco.2018.08.001
Publication status	Published - Dec 2018

Scopus Subject Areas

Algebra and Number Theory
Statistics and Probability
Numerical Analysis
General Mathematics
Control and Optimization
Applied Mathematics

User-Defined Keywords

Functional linear regression
Learning rate
Regularized least squares
Reproducing kernel Hilbert space

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10.1016/j.jco.2018.08.001

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title = "Analysis of regularized least squares for functional linear regression model",

abstract = "In this paper, we study and analyze the regularized least squares for functional linear regression model. The approach is to use the reproducing kernel Hilbert space framework and the integral operators. We show with a more general and realistic assumption on the reproducing kernel and input data statistics that the rate of excess prediction risk by the regularized least squares is minimax optimal.",

keywords = "Functional linear regression, Learning rate, Regularized least squares, Reproducing kernel Hilbert space",

author = "Hongzhi Tong and NG, {Kwok Po}",

note = "Funding Information: The authors thank the referees for their valuable comments and suggestions. The second author's research wassupported in part by HKRGC GRF, Hong Kong 12302715, 12306616, 12200317, and HKBU, Hong Kong RC-ICRS/16-17/03.",

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AU - NG, Kwok Po

N1 - Funding Information: The authors thank the referees for their valuable comments and suggestions. The second author's research wassupported in part by HKRGC GRF, Hong Kong 12302715, 12306616, 12200317, and HKBU, Hong Kong RC-ICRS/16-17/03.

PY - 2018/12

Y1 - 2018/12

N2 - In this paper, we study and analyze the regularized least squares for functional linear regression model. The approach is to use the reproducing kernel Hilbert space framework and the integral operators. We show with a more general and realistic assumption on the reproducing kernel and input data statistics that the rate of excess prediction risk by the regularized least squares is minimax optimal.

AB - In this paper, we study and analyze the regularized least squares for functional linear regression model. The approach is to use the reproducing kernel Hilbert space framework and the integral operators. We show with a more general and realistic assumption on the reproducing kernel and input data statistics that the rate of excess prediction risk by the regularized least squares is minimax optimal.

KW - Functional linear regression

KW - Learning rate

KW - Regularized least squares

KW - Reproducing kernel Hilbert space

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U2 - 10.1016/j.jco.2018.08.001

DO - 10.1016/j.jco.2018.08.001

M3 - Journal article

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VL - 49

SP - 85

EP - 94

JO - Journal of Complexity

JF - Journal of Complexity

ER -

Analysis of regularized least squares for functional linear regression model

Abstract

Scopus Subject Areas

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