A ν-Support Vector Quantile Regression Model with Automatic Accuracy Control

Abstract

Quantile regression models have become popular among researchers these days. These models are being used frequently for obtaining the probabilistic forecast in different real-world applications. The Support Vector Quantile Regression (SVQR) model can obtain the conditional quantile estimate using kernel function in a non-parametric framework. The ϵ-SVQR model successfully incorporates the concept of the asymmetric ϵ-insensitive tube in the SVQR model and enables it to obtain a sparse and accurate solution. But, it requires a good choice of the user-defined parameter. A bad choice of ϵ value may result in poor predictions in the ϵ-SVQR model. In this paper, we propose a novel ‘ν-Support Vector Quantile Regression’ (ν-SVQR) model for quantile estimation. It can efficiently obtain a suitable asymmetric ϵ-insensitive zone according to the variance present in the data. The proposed ν-SVQR model uses the ν fraction of training data points for the estimation of the quantiles. In the ν-SVQR model, training points asymptotically appear above and below the asymmetric ϵ-insensitive tube in the ratio of 1 − τ and τ. Apart from these, there are other interesting properties of the proposed ν-SVQR model, which we have briefly described in this paper. These properties have been empirically verified using simulated and real-world data sets also.