Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Inductive Inference: Theory and Methods
ACM Computing Surveys (CSUR)
Introduction to the Theory of Computation
Introduction to the Theory of Computation
An Introduction to the General Theory of Algorithms
An Introduction to the General Theory of Algorithms
On probably correct classification of concepts
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Classification using information
Annals of Mathematics and Artificial Intelligence
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Generalization is a learning problem that has received considerable attention. The generalization problem is to take a finite sample of some concept and produce an algorithm that can produce all other (perhaps infinitely many) samples of the same concept. Inductive inference is the study of this problem in a most general framework [1]. The classification problem is to take a finite sample of some concept and decide which type of concept the sample is from. The choice of type is usually finite. If the mechanism performing the classification is limiting, e.g., it makes more and more conjectures as to a classification as time goes on, then the process can also be considered as a type of learning. Roughly, we will say that some suitable mechanism has learned an appropriate classification if its sequence of conjectures stabilizes at some point. In this paper we formalize, at a suitable level of abstraction, the classification problem and rigorously compare it to the generalization problem. Despite some obvious similarities, the two notions are shown to be distinct. The new formalism of classification is investigated further.