Abstract

The fundamentals of an interface are presented to include prior knowledge in learning problems. This is done in the framework of regularization theory, working not with a restricted parameterization but directly with the function values itself. Technically, single components of prior knowledge are hereby represented by so called quadratic prior concepts. The error functional which has to be minimized is obtained by probabilistic or fuzzy logical operations of prior concepts. Commonly used regularization approaches correspond to a probabilistic implementaion of AND yielding convex error surfaces. The paper presents an approach to go beyond such classical regularization functionals by including OR-like combinations of prior concepts. Resulting in non-convex error functionals this requires non-linear stationarity equations to be solved. A great variety of corresponding learning algorithms can be constructed. The paper concentrates on the fundamental definitions.

Keywords: Prior information, Regularization, annealing methods, Landau-Ginzburg model.