Robustness analysis for Least Squares kernel based regression: an optimization approach

In kernel based regression techniques (such as Support Vector Machines or Least Squares Support Vector Machines) it is hard to analyze the influence of perturbed inputs on the estimates. We show that for a nonlinear black box model a convex problem can be derived if it is linearized with respect to the influence of input perturbations. For this model an explicit prediction equation can be found. The cast into a convex problem is possible as we assume that the perturbations are bounded by a design parameter ¿. The problem requires the solution of linear systems in Nd (the number of training points times the input dimensionality) variables. However, approximate solutions can be obtained with moderate computational effort. We demonstrate on simple examples that possible applications are in robust model selection, experiment design and model analysis.