On Robustness Properties of Convex Risk Minimization Methods for Pattern Recognition

The paper brings together methods from two disciplines: machine learning theory and robust statistics. Robustness properties of machine learning methods based on convex risk minimization are investigated for the problem of pattern recognition. Assumptions are given for the existence of the influence function of the classifiers and for bounds of the influence function. Kernel logistic regression, support vector machines, least squares and the AdaBoost loss function are treated as special cases. A sensitivity analysis of the support vector machine is given.