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
Probability and plurality for aggregations of learning machines
Information and Computation
Probabilistic inductive inference
Journal of the ACM (JACM)
Inductive inference with bounded number of mind changes
COLT '89 Proceedings of the second annual workshop on Computational learning theory
Relations between probabilistic and team one-shot learners (extended abstract)
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
On the role of procrastination in machine learning
Information and Computation
The strength of noninclusions for teams of finite learners (extended abstract)
COLT '94 Proceedings of the seventh annual conference on Computational learning theory
Breaking the probability 12 barrier in FIN-type learning
Journal of Computer and System Sciences
Finite identification of functions by teams with success ratio 1/2 and above
Information and Computation
Computational limits on team identification of languages
Information and Computation
Inductive Inference: Theory and Methods
ACM Computing Surveys (CSUR)
Probabilistic inductive inference: a survey
Theoretical Computer Science
Hierarchies of probabilistic and team FIN -learning
Theoretical Computer Science
An Introduction to the General Theory of Algorithms
An Introduction to the General Theory of Algorithms
On Identification by Teams and Probabilistic Machines
Algorithmic Learning for Knowledge-Based Systems, GOSLER Final Report
The power of procrastination in inductive inference: How it depends on used ordinal notations
EuroCOLT '95 Proceedings of the Second European Conference on Computational Learning Theory
The Power of Probabilism in Popperian FINite Learning (extended abstract)
AII '92 Proceedings of the International Workshop on Analogical and Inductive Inference
Use of Reduction Arguments in Determining Popperian FIN-Type Learning Capabilities
ALT '93 Proceedings of the 4th International Workshop on Algorithmic Learning Theory
Three Decades of Team Learning
AII '94 Proceedings of the 4th International Workshop on Analogical and Inductive Inference: Algorithmic Learning Theory
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We consider the probability hierarchy for Popperian FINite learning and study the general properties of this hierarchy. We prove that the probability hierarchy is decidable, i.e. there exists an algorithm that receives p"1 and p"2 and answers whether PFIN-type learning with the probability of success p"1 is equivalent to PFIN-type learning with the probability of success p"2. To prove our result, we analyze the topological structure of the probability hierarchy. We prove that it is well-ordered in descending ordering and order-equivalent to ordinal @e"0. This shows that the structure of the hierarchy is very complicated. Using similar methods, we also prove that, for PFIN-type learning, team learning and probabilistic learning are of the same power.