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
A universal inductive inference machine
Journal of Symbolic Logic
On the role of procrastination in machine learning
Information and Computation
Ordinal mind change complexity of language identification
Theoretical Computer Science
Inductive inference with procrastination: back to definitions
Fundamenta Informaticae
Classification using information
Annals of Mathematics and Artificial Intelligence
Unifying logic, topology and learning in parametric logic
Theoretical Computer Science - Algorithmic learning theory(ALT 2002)
Mind change efficient learning
Information and Computation
Mind change efficient learning
Information and Computation
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Most learning paradigms impose a particular syntax on the class of concepts to be learned; the chosen syntax can dramatically affect whether the class is learnable or not. For classification paradigms, where the task is to determine whether the underlying world does or does not have a particular property, how that property is represented has no implication on the power of a classifier that just outputs 1's or 0's. But is it possible to give a canonical syntactic representation of the class of concepts that are classifiable according to the particular criteria of a given paradigm? We provide a positive answer to this question for classification in the limit paradigms in a logical setting, with ordinal mind change bounds as a measure of complexity. The syntactic characterization that emerges enables to derive that if a possibly noncomputable classifier can perform the task assigned to it by the paradigm, then a computable classifier can also perform the same task. The syntactic characterization is strongly related to the difference hierarchy over the class of open sets of some topological space; this space is naturally defined from the class of possible worlds and possible data of the learning paradigm.