Coefficient-based <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml1" display="inline" overflow="scroll" altimg="si1.gif"><mml:msup><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msup></mml:math>-regularized regression with indefinite kernels and unbounded sampling

Guo, Qin; Wang, Cheng; Ye, Peixin

doi:10.1016/j.jat.2018.07.003

Cited by 2 publications

(1 citation statement)

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“…Under the moment hypothesis for unbounded sampling, theoretical analysis for least squares regression has been well studied with various techniques in an extensive literature (see Cai, 2013;Cai & Wang, 2013;Chu & Sun, 2013;Guo, Wang, & Ye, 2018;Guo & Ye, 2016;Guo & Wang, 2011;Guo & Zhou, 2013;He, 2014;He, Chen, & Li, 2014;Lv & Feng, 2012;Nie & Wang, 2016;Wang & Guo, 2012;Wang & Zhou, 2011). However, the results about regression induced by nonquadratic loss functions are very sparse.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Regression Algorithms with Unbounded Sampling

Tong

Gao

2020

Neural Computation

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In this letter, we study a class of the regularized regression algorithms when the sampling process is unbounded. By choosing different loss functions, the learning algorithms can include a wide range of commonly used algorithms for regression. Unlike the prior work on theoretical analysis of unbounded sampling, no constraint on the output variables is specified in our setting. By an elegant error analysis, we prove consistency and finite sample bounds on the excess risk of the proposed algorithms under regular conditions.

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Section: Introductionmentioning

confidence: 99%

Analysis of Regression Algorithms with Unbounded Sampling

Tong

Gao

2020

Neural Computation

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Optimality of the rescaled pure greedy learning algorithms

Zhang

Xing

2022

Int. J. Wavelets Multiresolut Inf. Process.

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We propose the Rescaled Pure Greedy Learning Algorithm (RPGLA) for solving the kernel-based regression problem. The computational complexity of the RPGLA is less than the Orthogonal Greedy Learning Algorithm (OGLA) and Relaxed Greedy Learning Algorithm (RGLA). We obtain the convergence rates of the RPGLA for continuous kernels. When the kernel is infinitely smooth, we derive a convergence rate that can be arbitrarily close to the best rate [Formula: see text] under a mild assumption of the regression function.

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Coefficient-based lq-regularized regression with indefinite kernels and unbounded sampling

Cited by 2 publications

References 18 publications

Analysis of Regression Algorithms with Unbounded Sampling

Analysis of Regression Algorithms with Unbounded Sampling

Optimality of the rescaled pure greedy learning algorithms

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