Learning in Friedberg numberings

Language and Automata Theory and Applications

2009

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Section: Definition 2 [20] Fix a Hypothesis Spacementioning

confidence: 99%

Section: Special Hypothesis Spacesmentioning

confidence: 99%

Section: Special Hypothesis Spacesmentioning

confidence: 99%

“…Proof. We give the proof for part (b) from [24], and refer the reader to the above paper for the proof of parts (a) and (c).…”

Section: Special Hypothesis Spacesmentioning

confidence: 99%

Section: Special Hypothesis Spacesmentioning

confidence: 99%

See 3 more Smart Citations

Hypothesis Spaces for Learning

Language and Automata Theory and Applications

2009

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Prescribed Learning of R.E. Classes

Lecture Notes in Computer Science

Stephan

2007

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Abstract. This work extends studies of Angluin, Lange and Zeugmann on the dependence of learning on the hypotheses space chosen for the class. In subsequent investigations, uniformly recursively enumerable hypotheses spaces have been considered. In the present work, the following four types of learning are distinguished: class-comprising (where the learner can choose a uniformly recursively enumerable superclass as hypotheses space), class-preserving (where the learner has to choose a uniformly recursively enumerable hypotheses space of the same class), prescribed (where there must be a learner for every uniformly recursively enumerable hypotheses space of the same class) and uniform (like prescribed, but the learner has to be synthesized effectively from an index of the hypothesis space). While for explanatory learning, these four types of learnability coincide, some or all are different for other learning criteria. For example, for conservative learning, all four types are different. Several results are obtained for vacillatory and behaviourally correct learning; three of the four types can be separated, however the relation between prescribed and uniform learning remains open. It is also shown that every (not necessarily uniformly recursively enumerable) behaviourally correct learnable class has a prudent learner, that is, a learner using a hypotheses space such that it learns every set in the hypotheses space. Moreover the prudent learner can be effectively built from any learner for the class.

Numberings Optimal for Learning

Lecture Notes in Computer Science

Stephan

2008

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This paper extends previous studies on learnability in non-acceptable numberings by considering the question: for which criteria which numberings are optimal, that is, for which numberings it holds that one can learn every learnable class using the given numbering as hypothesis space. Furthermore an effective version of optimality is studied as well. It is shown that the effectively optimal numberings for finite learning are just the acceptable numberings. In contrast to this, there are non-acceptable numberings which are optimal for finite learning and effectively optimal for explanatory, vacillatory and behaviourally correct learning. The numberings effectively optimal for explanatory learning are the K-acceptable numberings. A similar characterization is obtained for the numberings which are effectively optimal for vacillatory learning. Furthermore, it is studied which numberings are optimal for one and not for another criterion: among the criteria of finite, explanatory, vacillatory and behaviourally correct learning all separations can be obtained; however every numbering which is optimal for explanatory learning is also optimal for consistent learning.