A new asymmetric <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e5563" altimg="si26.svg"><mml:mi>ϵ</mml:mi></mml:math>-insensitive pinball loss function based support vector quantile regression model

Anand, Pritam; Rastogi, Reshma; Chandra, Suresh

doi:10.1016/j.asoc.2020.106473

Cited by 16 publications

(17 citation statements)

References 12 publications

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“…A novel -SVQR model uses the -insensitive pinball loss function for quantile estimation [ 1 ] to find the unknown value of and through the solution of QPPs in such a way: subject to: and where slack variables are and ; is the quantile; input parameters are .…”

Section: Related Workmentioning

confidence: 99%

“…A novel ε-SVQR model uses the ε-insensitive pinball loss function for quantile estimation [1] to find the unknown value of w and b through the solution of QPPs in such a way:…”

Section: "-Insensitive Support Vector Quantile Regression ("-Svqr)mentioning

confidence: 99%

“…In the similar pattern, Balasundaram and Prasad [ 4 ] have also proposed TSVR based variant named as robust TSVR with Huber loss which is solved by function iterative approach and Newton iterative with Armijo step size to less sensitivity of noise and outliers. To improve the sparseness and prediction ability of the regression model, Anand et al [ 1 ] have improved the -support vector quantile regression model ( -SVQR) by adding the regularization term for quantile estimation. The -SVQR model mainly focuses on the sparseness of the regression model.…”

Section: Introductionmentioning

confidence: 99%

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On Regularization Based Twin Support Vector Regression with Huber Loss

Gupta

2021

Neural Process Lett

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Twin support vector regression (TSVR) is generally employed with ε-insensitive loss function which is not well capable to handle the noises and outliers. According to the definition, Huber loss function performs as quadratic for small errors and linear for others and shows better performance in comparison to Gaussian loss hence it restrains easily for a different type of noises and outliers. Recently, TSVR with Huber loss (HN-TSVR) has been suggested to handle the noise and outliers. Like TSVR, it is also having the singularity problem which degrades the performance of the model. In this paper, regularized version of HN-TSVR is proposed as regularization based twin support vector regression (RHN-TSVR) to avoid the singularity problem of HN-TSVR by applying the structured risk minimization principle that leads to our model convex and well-posed. This proposed RHN-TSVR model is well capable to handle the noise as well as outliers and avoids the singularity issue. To show the validity and applicability of proposed RHN-TSVR, various experiments perform on several artificial generated datasets having uniform, Gaussian and Laplacian noise as well as on benchmark different real-world datasets and compare with support vector regression, TSVR, ε-asymmetric Huber SVR, ε-support vector quantile regression and HN-TSVR. Here, all benchmark real-world datasets are embedded with a different significant level of noise 0%, 5% and 10% on different reported algorithms with the proposed approach. The proposed algorithm RHN-TSVR is showing better prediction ability on artificial datasets as well as real-world datasets with a different significant level of noise compared to other reported models.

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Section: Related Workmentioning

confidence: 99%

“…A novel ε-SVQR model uses the ε-insensitive pinball loss function for quantile estimation [1] to find the unknown value of w and b through the solution of QPPs in such a way:…”

Section: "-Insensitive Support Vector Quantile Regression ("-Svqr)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Regularization Based Twin Support Vector Regression with Huber Loss

Gupta

2021

Neural Process Lett

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“…Furthermore, ( , ) and ( , ) refer to real and imaginary dual variables vectors in time and frequency-domains, respectively. It is straightforward to show that the weights solution can be determined by optimizing the formulation (30) with respect to variables (1,2) ,( , ) , (1,2) * ,( , ) , (1,2) ,( , ) , (1,2) * , ( , ) and afterward substituting into (26) and (27), respectively.…”

Section: Dual Problems Representationmentioning

confidence: 99%

“…Melki et al [25] examined multi-target regression and provided some models for multiple-outputs problems. Anand et al [26] studied the pinball loss function in the SVR algorithm. In [27], authors examined the Lagrangian SVR problems.…”

Section: Introductionmentioning

confidence: 99%

Twin Support Vector Regression for complex millimetric wave propagation environment

Charrada

Samet

2020

Heliyon

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In this article, an effective millimetric wave channel estimation algorithm based on Twin Support Vector Regression (TSVR) is proposed. This algorithm exploits Discrete Wavelet Transform (DWT) in order to denoise samples in learning phase and then enhance fitting performance. An indoor complex conference room environment full of furniture and electronic equipments is adopted for experiments. Through the proposed approach, channel frequency responses are directly estimated using the Orthogonal Frequency Division Multiplexing (OFDM) reference symbol pattern by solving two quadratic programming problems in order to improve generalization aptitude and computational speed. We consider in this work a Channel Impulse Response (CIR) of 60 GHz multipath transmission system generated by the "Wireless InSite" ray tracer by Remcom. The numerical experiments confirm the performance of the proposed approach compared to other conventional algorithms for several configuration scenarios with and without mobility.

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A novel support vector machine with generalized pinball loss for uncertain data classification

Damminsed,

Panup,

Makmuang

et al. 2023

Math Methods in App Sciences

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In real‐world problems, data suffer from measurement errors, data staleness, and repeated measurements, which make data uncertain. To consider the uncertainty of data, the concept of giving each data feature as a multidimensional Gaussian distribution has been utilized. In 2021, support vector machines with an insensitive zone pinball loss (UPinSVMs) for uncertain data classification was proposed, where is a positive number. The UPinSVMs bring noise insensitivity, stability for resampling, and increased model sparsity. However, the value of is known to be specified. In order to improve the performance, we combine the generalized pinball loss (( ‐Mod‐Pin‐SVM) into the uncertain classification, term as UGPinSVMs, where are two positive numbers. The generalized pinball loss is an optimal insensitive zone pinball loss and is an extension of existing loss functions that also addresses the issues of noise insensitivity and resampling instability. We solve the primal quadratic programming problems by transforming individuals into unconstrained optimization using an efficient stochastic gradient descent algorithm. More specially, we have introduced verified theorems that are related to our approaches and investigated scatter minimization. The results from several benchmark datasets show that our model outperforms the existing classifier in terms of accuracy and statistical analysis. Furthermore, the application of our framework to the crop recommendation dataset is also examined.

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A new asymmetric ϵ-insensitive pinball loss function based support vector quantile regression model

Cited by 16 publications

References 12 publications

On Regularization Based Twin Support Vector Regression with Huber Loss

On Regularization Based Twin Support Vector Regression with Huber Loss

Twin Support Vector Regression for complex millimetric wave propagation environment

A novel support vector machine with generalized pinball loss for uncertain data classification

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