Convergence rate of SVM for kernel-based robust regression

Wang, Shuhua; Chen, Zhenlong; Sheng, Baohuai

doi:10.1142/s0219691319500048

Cited by 7 publications

(3 citation statements)

References 30 publications

(23 reference statements)

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“…The quadratic loss function is not a strongly convex function, we have relaxed the strong convexity assumption in the literature [26]. And our method may be extended to some online pairwise learning algorithms with non-convex loss functions, e.g., the robust loss function in [62].…”

Section: Further Discussionmentioning

confidence: 99%

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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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Section: Further Discussionmentioning

confidence: 99%

“…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%

Convergence of online pairwise regression learning with quadratic loss

Wang¹,

Chen²,

Sheng³

2020

Communications on Pure &Amp; Applied Analysis

Self Cite

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“…Support vector machines (SVMs) are well-known for their effectiveness in classification and regression [ 10 , 25 , 26 ]. Shuhua et al [ 27 ] developed a technique for assessing the error in kernel regularized regression using a non-convex loss function, which minimizes the negative impact of outliers on its performance. Despite the experience of radiologists, predicting infections using medical imaging is challenging due to the lack of detailed disease knowledge.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous Super-Resolution and Classification of Lung Disease Scans

et al. 2023

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Acute lower respiratory infection is a leading cause of death in developing countries. Hence, progress has been made for early detection and treatment. There is still a need for improved diagnostic and therapeutic strategies, particularly in resource-limited settings. Chest X-ray and computed tomography (CT) have the potential to serve as effective screening tools for lower respiratory infections, but the use of artificial intelligence (AI) in these areas is limited. To address this gap, we present a computer-aided diagnostic system for chest X-ray and CT images of several common pulmonary diseases, including COVID-19, viral pneumonia, bacterial pneumonia, tuberculosis, lung opacity, and various types of carcinoma. The proposed system depends on super-resolution (SR) techniques to enhance image details. Deep learning (DL) techniques are used for both SR reconstruction and classification, with the InceptionResNetv2 model used as a feature extractor in conjunction with a multi-class support vector machine (MCSVM) classifier. In this paper, we compare the proposed model performance to those of other classification models, such as Resnet101 and Inceptionv3, and evaluate the effectiveness of using both softmax and MCSVM classifiers. The proposed system was tested on three publicly available datasets of CT and X-ray images and it achieved a classification accuracy of 98.028% using a combination of SR and InceptionResNetv2. Overall, our system has the potential to serve as a valuable screening tool for lower respiratory disorders and assist clinicians in interpreting chest X-ray and CT images. In resource-limited settings, it can also provide a valuable diagnostic support.

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Learning Rates of Kernel-Based Robust Classification

Wang

Sheng

2022

Acta Math Sci

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Convergence rate of SVM for kernel-based robust regression

Cited by 7 publications

References 30 publications

Convergence of online pairwise regression learning with quadratic loss

Convergence of online pairwise regression learning with quadratic loss

Simultaneous Super-Resolution and Classification of Lung Disease Scans

Learning Rates of Kernel-Based Robust Classification

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