A new asymmetric $\epsilon$-insensitive pinball loss function based support vector quantile regression model

TL;DR

This paper introduces a novel asymmetric epsilon-insensitive pinball loss function for support vector quantile regression, enhancing prediction accuracy and sparsity, validated through experiments on artificial and real datasets.

Contribution

The paper proposes a new asymmetric epsilon-insensitive pinball loss function that improves quantile estimation and sparsity in support vector quantile regression models.

Findings

Significantly improves prediction accuracy in SVQR.

Restores sparsity in the SVQR model.

Demonstrates superior performance on various datasets.

Abstract

In this paper, we propose a novel asymmetric $\epsilon$-insensitive pinball loss function for quantile estimation. There exists some pinball loss functions which attempt to incorporate the $\epsilon$-insensitive zone approach in it but, they fail to extend the $\epsilon$-insensitive approach for quantile estimation in true sense. The proposed asymmetric $\epsilon$-insensitive pinball loss function can make an asymmetric $\epsilon$- insensitive zone of fixed width around the data and divide it using $\tau$ value for the estimation of the $\tau$th quantile. The use of the proposed asymmetric $\epsilon$-insensitive pinball loss function in Support Vector Quantile Regression (SVQR) model improves its prediction ability significantly. It also brings the sparsity back in SVQR model. Further, the numerical results obtained by several experiments carried on artificial and real world datasets empirically show the efficacy of the proposed `$\epsilon$-Support Vector Quantile Regression' ($\epsilon$-SVQR) model over other existing SVQR models.