Convex Support Vector Regression

TL;DR

This paper introduces convex support vector regression (CSVR), a novel method that improves nonparametric convex regression by enhancing robustness and reducing overfitting, with demonstrated superior performance in experiments.

Contribution

The paper presents CSVR, integrating convex regression and support vector regression to address overfitting and outliers in nonparametric convex regression.

Findings

CSVR outperforms existing methods in prediction accuracy.

CSVR demonstrates increased robustness to outliers.

Numerical experiments validate the effectiveness of CSVR.

Abstract

Nonparametric regression subject to convexity or concavity constraints is increasingly popular in economics, finance, operations research, machine learning, and statistics. However, the conventional convex regression based on the least squares loss function often suffers from overfitting and outliers. This paper proposes to address these two issues by introducing the convex support vector regression (CSVR) method, which effectively combines the key elements of convex regression and support vector regression. Numerical experiments demonstrate the performance of CSVR in prediction accuracy and robustness that compares favorably with other state-of-the-art methods.