Ordinal mind change complexity of language identification

Ambainis, Andris; Jain, Sanjay; Sharma, Arun

doi:10.1007/3-540-62685-9_25

Cited by 10 publications

(1 citation statement)

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“…Subsequently to [CJS95], natural O-notations for constructive ordinals polynomial in m have been extensively employed to provide natural classifications of standard problems within the context of learning grammars for formal languages [JS97], [AJS99], [JS99].…”

Section: Using Notations For Constructive Ordinals As Parsimony Measumentioning

confidence: 99%

Parsimony hierarchies for inductive inference

Ambainis¹,

Case²,

Jain³

et al. 2004

J. symb. log.

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Freivalds defined an acceptable programming system independent criterion for learning programs for functions in which the final programs were required to be both correct and "nearly" minimal size, i.e, within a computable function of being purely minimal size. Kinber showed that this parsimony requirement on final programs limits learning power. However, in scientific inference, parsimony is considered highly desirable. A lim-computable function is (by definition) one calculable by a total procedure allowed to change its mind finitely many times about its output. Investigated is the possibility of assuaging somewhat the limitation on learning power resulting from requiring parsimonious final programs by use of criteria which require the final, correct programs to be "not-so-nearly" minimal size, e.g., to be within a lim-computable function of actual minimal size. It is shown that some parsimony in the final program is thereby retained, yet learning power strictly increases. Considered, then, are lim-computable functions as above but for which notations for constructive ordinals are used to bound the number of mind changes allowed regarding the output. This is a variant of an idea introduced by Freivalds and Smith. For this ordinal notation complexity bounded version of lim-computability, the power of the resultant learning criteria form finely graded, infinitely ramifying, infinite hierarchies intermediate between the computable and the lim-computable cases. Some of these hierarchies, for the natural notations determining them, are shown to be optimally tight.

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Section: Using Notations For Constructive Ordinals As Parsimony Measumentioning

confidence: 99%

Parsimony hierarchies for inductive inference

Ambainis¹,

Case²,

Jain³

et al. 2004

J. symb. log.

Self Cite

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On a Generalized Notion of Mistake Bounds

Jain

Sharma

2001

Information and Computation

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This paper proposes the use of constructive ordinals as mistake bounds in the on-line learning model. This approach elegantly generalizes the applicability of the on-line mistake bound model to learnability analysis of very expressive concept classes like pattern languages, unions of pattern languages, elementary formal systems, and minimal models of logic programs. The main result in the paper shows that the topological property of effective finite bounded thickness is a sufficient condition for on-line learnability with a certain ordinal mistake bound. An interesting characterization of the on-line learning model is shown in terms of the identification in the limit framework. It is established that the classes of languages learnable in the on-line model with a mistake bound of α are exactly the same as the classes of languages learnable in the limit from both positive and negative data by a Popperian, consistent learner with a mind change bound of α. This result nicely builds a bridge between the two models.

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On Learning Unions of Pattern Languages and Tree Patterns

Goldman

Kwek

1999

Lecture Notes in Computer Science

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Ordinal mind change complexity of language identification

Cited by 10 publications

References 20 publications

Parsimony hierarchies for inductive inference

Parsimony hierarchies for inductive inference

On a Generalized Notion of Mistake Bounds

On Learning Unions of Pattern Languages and Tree Patterns

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