Robust linear and support vector regression

The robust Huber M-estimator, a differentiable cost function that is quadra tic for small errors and linear otherwise, is modeled exactly, in the origi nal primal space of the problem, by an easily solvable simple convex quadra tic program for both linear and nonlinear support vector estimators. Previo us models were significantly more complex or formulated in the dual space a nd most involved specialized numerical algorithms for solving the robust Hu ber 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 suppo rt vector problems. Results are shown on problems with as many as 20,000 da ta points, with considerably faster running times on larger problems.