A thesis in inductive inference

Wiehagen, Rolf

doi:10.1007/bfb0023324

Cited by 54 publications

(38 citation statements)

References 17 publications

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“…For finite learning with and without the oracle K we obtain a characterization in terms of fully isolated branches on recursively enumerable trees and we show that strong-monotonic BC, as introduced by Wiehagen [22], can be characterized in terms of the isolated branches on a single recursive tree.…”

Section: Article In Pressmentioning

confidence: 99%

“…Wiehagen [22] introduced the concept of strong-monotonic learning of functions. A machine M infers a function f strong-monotonically if and only if for all s and t with s%t%f we have j MðsÞ ðxÞk ¼ y ) j MðtÞ ðxÞk ¼ y (hence in particular j MðsÞ ðxÞ ¼ f ðxÞ whenever j MðsÞ ðxÞ is defined for some s%f ).…”

Section: Finite Learning and Single Treesmentioning

confidence: 99%

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Trees and learning

Merkle

Stephan

2004

Journal of Computer and System Sciences

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We characterize FIN-, EX-and BC-learning, as well as the corresponding notions of team learning, in terms of isolated branches on effectively given sequences of trees. The more restrictive models of FINlearning and strong-monotonic BC-learning are characterized in terms of isolated branches on a single tree. Furthermore, we discuss learning with additional information where the learner receives an index for a strongly recursive tree such that the function to be learned is isolated on this tree. We show that EXlearning with this type of additional information is strictly more powerful than EX-learning. r

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Section: Article In Pressmentioning

confidence: 99%

Section: Finite Learning and Single Treesmentioning

confidence: 99%

Trees and learning

Merkle

Stephan

2004

Journal of Computer and System Sciences

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“…Effective learning is related to monotonic learning Zeugmann 1993, 1994;Kinber 1994;Zeugmann et al 1995) originally introduced by Jantke (1991), Wiehagen (1991), since both learning models consider monotonic convergence of hypotheses. In contrast to their approach, where various monotonicity over languages was considered, we geometrically measure the generalization error of a hypothesis by the Hausdorff metric.…”

Section: Effective Learning Of Figuresmentioning

confidence: 99%

Learning figures with the Hausdorff metric by fractals—towards computable binary classification

et al. 2012

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“…Note that the following example can be transferred to many related notions like monotonic [22] and non U-shaped learning [2] without giving more insight. Therefore, these learning criteria are not considered in the present work.…”

Section: Finite and Explanatory Learningmentioning

confidence: 99%

Prescribed Learning of R.E. Classes

Jain

Stephan

2007

Lecture Notes in Computer Science

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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.

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A thesis in inductive inference

Cited by 54 publications

References 17 publications

Trees and learning

Trees and learning

Learning figures with the Hausdorff metric by fractals—towards computable binary classification

Prescribed Learning of R.E. Classes

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