A $\nu$- support vector quantile regression model with automatic accuracy control

TL;DR

This paper introduces a $ u$-support vector quantile regression model that automatically adjusts accuracy through an asymmetric insensitivity zone, effectively estimating quantiles with a data-driven approach.

Contribution

It presents a novel $ u$-SVQR model that controls accuracy automatically and asymptotically balances data points around the quantile estimate, verified on artificial and real datasets.

Findings

Model effectively estimates quantiles with automatic accuracy control.

Asymptotic distribution of training points aligns with theoretical ratios.

Empirical validation confirms the model's properties on diverse datasets.

Abstract

This paper proposes a novel '$\nu$-support vector quantile regression' ($\nu$-SVQR) model for the quantile estimation. It can facilitate the automatic control over accuracy by creating a suitable asymmetric $\epsilon$-insensitive zone according to the variance present in data. The proposed $\nu$-SVQR model uses the $\nu$ fraction of training data points for the estimation of the quantiles. In the $\nu$-SVQR model, training points asymptotically appear above and below of the asymmetric $\epsilon$-insensitive tube in the ratio of $1-\tau$ and $\tau$. Further, there are other interesting properties of the proposed $\nu$-SVQR model, which we have briefly described in this paper. These properties have been empirically verified using the artificial and real world dataset also.