Complexity theory of real functions
Complexity theory of real functions
Decision theoretic generalizations of the PAC model for neural net and other learning applications
Information and Computation
On the inductive inference of real valued functions
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
Inferability of Recursive Real-Valued Functions
ALT '97 Proceedings of the 8th International Conference on Algorithmic Learning Theory
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In this paper we investigate inductive inference of recursive real-valued functions from data. A recursive real-valued function is regarded as a computable interval mapping, which has been introduced by Hirowatari and Arikawa (1997), and modified by Apsitis et al (1998). The learning model we consider in this paper is an extension of the Gold's inductive inference. We first introduce some criteria for successful inductive inference of recursive real-valued functions. Then we show a recursively enumerable class of recursive real-valued functions which is not inferable in the limit. This should be an interesting contrast to the result by Wiehagen (1976) that every recursively enumerable subset of recursive functions from N to N is consistently inferable in the limit. We also show that every recursively enumerable class of recursive real-valued functions on a fixed rational interval is consistently inferable in the limit. Furthermore we show that our consistent inductive inference coincides with the ordinary inductive inference, when we deal with recursive real-valued functions on a fixed closed rational interval.