On the inductive inference of recursive real-valued functions

Authors: Kalvis Apsitis, Setsuo Arikawa, Rusins Freivalds, Eiju Hirowatari and Carl H. Smith

Source: Theoretical Computer Science Vol. 219, No. 1/2, 1999, 3 - 17.

Abstract. We combine traditional studies of inductive inference and classical continuous mathematics to produce a study of learning real-valued functions. We consider two possible ways to model the learning by example of functions with domain and range the real numbers. The first approach considers functions as represented by computable analytic functions. The second considers arbitrary computable functions of recursive real numbers. In each case we find natural examples of learnable classes of functions and unlearnable classes of functions.

©Copyright 1999, Elsevier Science.