Systems that learn: an introduction to learning theory for cognitive and computer scientists
Systems that learn: an introduction to learning theory for cognitive and computer scientists
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
International Workshop All '86 on Analogical and inductive inference
On the role of search for learning
COLT '89 Proceedings of the second annual workshop on Computational learning theory
One-sided error probabilistic inductive inference and reliable frequency identification
Information and Computation
Robust behaviorally correct learning
Information and Computation
A Machine-Independent Theory of the Complexity of Recursive Functions
Journal of the ACM (JACM)
Robust learning aided by context
Journal of Computer and System Sciences - Eleventh annual conference on computational learning theory&slash;Twelfth Annual IEEE conference on computational complexity
Inductive Inference: Theory and Methods
ACM Computing Surveys (CSUR)
Journal of Computer and System Sciences
Transformations that Preserve Learnability
ALT '96 Proceedings of the 7th International Workshop on Algorithmic Learning Theory
A Thesis in Inductive Inference
Proceedings of the 1st International Workshop on Nonmonotonic and Inductive Logic
Inductive Inference of Recursive Functions: Qualitative Theory
Baltic Computer Science, Selected Papers
Learning recursive functions: A survey
Theoretical Computer Science
Consistent and coherent learning with δ-delay
Information and Computation
Consistency conditions for inductive inference of recursive functions
JSAI'06 Proceedings of the 20th annual conference on New frontiers in artificial intelligence
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Blum and Blum (Inform. and Control 28 (1975) 125-155) showed that a class B of suitable recursive approximations to the halting problem K is reliably EX-learnable but left it open whether or not B is in NUM. By showing B to be not in NUM we resolve this old problem.Moreover, variants of this problem obtained by approximating any given recursively enumerable set A instead of the halting problem K are studied. All corresponding function classes U(A) are still EX-inferable but may fail to be reliably EX-learnable, for example if A is non-high and hypersimple.Blum and Blum (1975) considered only approximations to K defined by monotone complexity functions. We prove this condition to be necessary for making learnability independent of the underlying complexity measure. The class B of all recursive approximations to K generated by all total complexity functions is shown to be not even behaviorally correct learnable for a class of natural complexity measures. On the other hand, there are complexity measures such that B is EX-learnable. A similar result is obtained for all classes U(A).For natural complexity measures, B is shown to be not robustly learnable, but again there are complexity measures such that B and, more generally, every class U(A) is robustly EX-learnable. This result extends the criticism of Jain et al. (J. Comput. System Sci. 62(1) (2001) 178-212), since the classes defined by artificial complexity measures turn out to be robustly learnable while those defined by natural complexity measures are not robustly learnable.