Heidelberg 1999 – scientific programme

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KY: Kybernetik

KY 5: Weitere Beiträge (Artikel)

KY 5.1: Poster

Monday, March 15, 1999, 13:00–14:00, ZO 3

Empirical learning with ambiguous a priori information — •Jörg Lemm — Institut für Theoretische Physik I, University of Münster

Learning continuous functions from a finite number of empirical data is not a well defined problem without additional restrictions or a priori information. In most learning systems the necessary restrictions are given implicitly by using parameterized function spaces making an explicit interpretation difficult or impossible. Historically, the development of empirical learning systems went over parametric methods with small number of parameters (e.g., linear regression) to nonparametric methods with very large number of parameters (e.g., neural networks). Recently now stochastic process and regularization approaches have been become popular which treat the (infinite number of) individual function values itself as fundamental parameters. This has the advantage that a priori information can be expressed explicitly in terms of the function values of interest. However, nearly all regularization approaches use quadratic, and therefore convex, error functionals. Ambiguous a priori information is a typical case which requires in general non–convex error functionals. Ambiguous a priori information is here understood as a situation where a set of possible alternative priors is given but the actual prior realized from this set is unknown. The paper presents methods related to statistical field theory to go beyond classical quadratic regularization approaches.