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On the inductive inference of recursive real-valued functions

✍ Scribed by Kalvis Apsītis; Setsuo Arikawa; Rũsiņš Freivalds; Eiju Hirowatari; Carl H. Smith

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
894 KB
Volume
219
Category
Article
ISSN
0304-3975

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✦ Synopsis

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.

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✍ Peter L. Bartlett; Philip M. Long; Robert C. Williamson 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 1011 KB

We consider the problem of learning real-valued functions from random examples when the function values are corrupted with noise. With mild conditions on independent observation noise, we provide characterizations of the learnability of a real-valued function class in terms of a generalization of th