Machine Learning Under Stochastic Uncertainty

New methods for machine learning under stochastic uncertainty, especially for regression problems under uncertainty are described in this chapter. Given a set of input-output data, a certain, often parametric set of functions is adapted by evaluating and then minimizing the approximation error by quadratic cost functions. Here, instead of quadratic cost functions, sublinear cost functions, involving, e.g., the maximum absolute error, are taken into account. In this case the regression problem under stochastic uncertainty yields a stochastic linear program with a dual decomposition data structure which enables the use of very efficient linear programming algorithms. Two and multi-group classification problems are considered in the second part of this chapter. Here, the separation of the data points in a certain space \(\mathbb {R}^n\) and the representation of the groups or classes of data points is described by means of hyperplanes in \(\mathbb {R}^n\) . Instead of the often used discrete data points, for the classification process convex or stochastic convex hulls of the given data points are taken into account.