Robust Linear and Support Vector Regression

Abstract

The robust Huber M-estimator, a differentiable cost function that is quadratic for small errors and linear otherwise, is modeled exactly, in the original primal space of the problem, by an easily solvable simple convex quadratic program for both linear and nonlinear support vector estimators. Previous models were significantly more complex or formulated in the dual space and most involved specialized numerical algorithms for solving the robust Huber linear estimator [3], [6], [12], [13], [14], [23], [28]. Numerical test comparisons with these algorithms indicate the computational effectiveness of the new quadratic programming model for both linear and nonlinear support vector problems. Results are shown on problems with as many as 20,000 data points, with considerably faster running times on larger problems.