The convergence rate of semi-supervised regression with quadratic loss

It is known that to alleviate the performance deterioration caused by the outliers, the robust support vector (SV) regression is proposed, which is essentially a convex optimization problem associated with a non-convex loss function. The theory analysis for its performance cannot be finished by the usual convex analysis approach. For a robust SV regression algorithm containing two homotopy parameters, a non-convex method is developed with the quasiconvex analysis theory and the error estimate is given. An explicit convergence rate is provided, and the effect degree of outliers on the performance is quantitatively shown.

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“…where assume that the K-functional satisfies certain decay, for example, we assume [3][4][5][6]25,35…”

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confidence: 99%

Convergence rate of SVM for kernel-based robust regression

Wang

Chen

Sheng

2019

Int. J. Wavelets Multiresolut Inf. Process.

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“…In learning theory, we often assume the K-functionals satisfy certain decay, for example, we assume (see e.g. [53,55,56,62]).…”

Section: By (23) We Havementioning

confidence: 99%

“…On the other hand, we find that the quadratic function √ 1 + t 2 , t ∈ R plays an important role in constructing shape preserving quasi-interpolation and solving partial differential equations with meshfree method since its strong nonlinear property and its convexity(see [14,25,66,67]), and it has been used by [56] as the loss function which shows some advantages in forming semi-supervised learning algorithms. Encouraged by these researches, we want to make an investigation on how these parameters influence the learning rates of the online pairwise learning.…”

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Convergence of online pairwise regression learning with quadratic loss

Wang¹,

Chen²,

Sheng³

2020

Communications on Pure &Amp; Applied Analysis

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Recent investigations on the error analysis of kernel regularized pairwise learning initiate the theoretical research on pairwise reproducing kernel Hilbert spaces (PRKHSs). In the present paper, we provide a method of constructing PRKHSs with classical Jacobi orthogonal polynomials. The performance of the kernel regularized online pairwise regression learning algorithms based on a quadratic loss function is investigated. Applying convex analysis and Rademacher complexity techniques, the bounds for the generalization error are provided explicitly. It is shown that the convergence rate can be greatly improved by adjusting the scale parameters in the loss function.1. Introduction. In recent years, online learning algorithms have been attracting the attentions of a lot of researchers in statistical learning theory(see e.g. [21,58,71,73,74] and references therein). In present paper, we shall give an investigation on the convergence analysis of kernel-based regularized online pairwise learning algorithm associating with the quadratic loss.1.1. Online learning algorithms. Let X be a given compact set in the d-dimensional Euclidean space R d , Y ⊂ R. Let ρ be a fixed but unknown probability distribution on Z = X × Y which yields its marginal distribution ρ x on X and its conditional distribution ρ(• | x) at x ∈ X. Then we denote by {z t = (x t , y t )} T t=1 the sample drawn i.i.d.(independently and identically distribution) according to distribution ρ. The aim of regression learning is to find a predictor f : X → R from a hypothesis space such that f (x) is a "good" approximation of y. Let V (r) : R → R +

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“…Many mathematicians have paid their attentions to this field (see e.g. [18] [19] [21] [25] [26] [27] [28]).…”

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Solving Neumann Boundary Problem with Kernel-Regularized Learning Approach

Ran,

Sheng

2024

JAMP

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We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.

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The convergence rate of semi-supervised regression with quadratic loss

Cited by 9 publications

References 23 publications

Convergence rate of SVM for kernel-based robust regression

Convergence rate of SVM for kernel-based robust regression

Convergence of online pairwise regression learning with quadratic loss

Solving Neumann Boundary Problem with Kernel-Regularized Learning Approach

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