Improvement over Pinball Loss Support Vector Machine

Recently, there have been several papers that discuss the extension of the Pinball loss Support Vector Machine (Pin-SVM) model, originally proposed by Huang et al.,[1][2]. Pin-SVM classifier deals with the pinball loss function, which has been defined in terms of the parameter $\tau$. The parameter $\tau$ can take values in $[ -1,1]$. The existing Pin-SVM model requires to solve the same optimization problem for all values of $\tau$ in $[ -1,1]$. In this paper, we improve the existing Pin-SVM model for the binary classification task. At first, we note that there is major difficulty in Pin-SVM model (Huang et al. [1]) for $ -1 \leq \tau < 0$. Specifically, we show that the Pin-SVM model requires the solution of different optimization problem for $ -1 \leq \tau < 0$. We further propose a unified model termed as Unified Pin-SVM which results in a QPP valid for all $-1\leq \tau \leq 1$ and hence more convenient to use. The proposed Unified Pin-SVM model can obtain a significant improvement in accuracy over the existing Pin-SVM model which has also been empirically justified by extensive numerical experiments with real-world datasets.

Learning a powerful SVM using piece-wise linear loss functions

In this paper, we have considered general k-piece-wise linear convex loss functions in SVM model for measuring the empirical risk. The resulting k-Piece-wise Linear loss Support Vector Machine (k-PL-SVM) model is an adaptive SVM model which can learn a suitable piece-wise linear loss function according to nature of the given training set. The k-PL-SVM models are general SVM models and existing popular SVM models, like C-SVM, LS-SVM and Pin-SVM models, are their particular cases. We have performed the extensive numerical experiments with k-PL-SVM models for k = 2 and 3 and shown that they are improvement over existing SVM models.

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

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.

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

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.

Support Vector Regression via a Combined Reward Cum Penalty Loss Function

In this paper, we introduce a novel combined reward cum penalty loss function to handle the regression problem. The proposed combined reward cum penalty loss function penalizes the data points which lie outside the $\epsilon$-tube of the regressor and also assigns reward for the data points which lie inside of the $\epsilon$-tube of the regressor. The combined reward cum penalty loss function based regression (RP-$\epsilon$-SVR) model has several interesting properties which are investigated in this paper and are also supported with the experimental results.