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
On the inductive inference of recursive real-valued functions
Theoretical Computer Science - Special issue on computability and complexity in analysis
Inferability of Recursive Real-Valued Functions
ALT '97 Proceedings of the 8th International Conference on Algorithmic Learning Theory
Learning figures with the hausdorff metric by fractals
ALT'10 Proceedings of the 21st international conference on Algorithmic learning theory
Prediction of recursive real-valued functions from finite examples
JSAI'05 Proceedings of the 2005 international conference on New Frontiers in Artificial Intelligence
| Hi-index | 0.00 |
In this paper we investigate the inductive inference of recursive real-valued functions from data. A recursive real-valued function is regarded as a computable interval mapping. The learning model we consider in this paper is an extension of 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, Elektronische Informationsverarbeitung und Kybernetik, Vol. 12, pp. 93--99) 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. Copyright 2001 Elsevier Science B.V. All rights reserved.