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A mathematical framework for learning and adaption: (generalized) random systems with complete connections.

Ulrich Herkenrath;  Radu Theodorescu — 1981

Trabajos de Estadística e Investigación Operativa

The aim of this paper is to show that the theory of (generalized) random systems with complete connection may serve as a mathematical framework for learning and adaption. Chapter 1 is of an introductory nature and gives a general description of the problems with which one is faced. In Chapter 2 the mathematical model and some results about it are explained. Chapter 3 deals with special learning and adaption models.

On integer stochastic approximation

Václav Dupač;  Ulrich Herkenrath — 1984

Aplikace matematiky

Let M : 𝐑 → 𝐑 be observable, with experimental errors, at integer points only; unknown elsewhere. Iterative nonparametric procedures for finding the zero point of M are called procedures of integer stochastic approximation. Three types of such procedures (Derman’s, Mukerjee’s and the authors’) are described and compared. A two-dimensional analogue of the third approach is proposed and investigated; its generalization to higher dimensions is conjectured.

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