Not-so-nearly-minimal-size program inference (preliminary report)

Theoretical Computer Science

2002

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Section: Ordinal Mind Change Identificationmentioning

confidence: 99%

Mind change complexity of learning logic programs

Theoretical Computer Science

2002

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“…We do not go into the details of the notation system used, but instead refer the reader to [Kle38,Rog67,Sac90,CJS95,FS93]. In the sequel, we are somewhat informal and use +, ×, and for all m ∈ N as notation for the same.…”

Section: Notationmentioning

confidence: 99%

On a generalized notion of mistake bounds

Proceedings of the Twelfth Annual Conference on Computational Learning Theory

1999

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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.

“…Similarly, × O and + O refer to the addition and multiplication of the ordinal notations in this system. We do not go into the details of the notation system used, but instead refer the reader to [19,27,28,6,9].…”

Section: Ordinals As Mind Change Countersmentioning

confidence: 99%

Ordinal mind change complexity of language identification

Ambainis

Lecture Notes in Computer Science

1997

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The approach of ordinal mind change complexity, introduced by Freivalds and Smith, uses (notations for) constructive ordinals to bound the number of mind changes made by a learning machine. This approach provides a measure of the extent to which a learning machine has to keep revising its estimate of the number of mind changes it will make before converging to a correct hypothesis for languages in the class being learned. Recently, this notion, which also yields a measure for the difficulty of learning a class of languages, has been used to analyze the learnability of rich concept classes.The present paper further investigates the utility of ordinal mind change complexity. It is shown that for identification from both positive and negative data and n ≥ 1, the ordinal mind change complexity of the class of languages formed by unions of up to n + 1 pattern languages is only ω × O notn(n) (where notn(n) is a notation for n, ω is a notation for the least limit ordinal and × O represents ordinal multiplication). This result nicely extends an observation of Lange and Zeugmann that pattern languages can be identified from both positive and negative data with 0 mind changes.Existence of an ordinal mind change bound for a class of learnable languages can be seen as an indication of its learning "tractability." Conditions are investigated under which a class has an ordinal mind change bound for identification from positive data. It is shown that an indexed family of languages has an ordinal mind Preprint submitted to Elsevier Science change bound if it has finite elasticity and can be identified by a conservative machine. It is also shown that the requirement of conservative identification can be sacrificed for the purely topological requirement of M -finite thickness. Interaction between identification by monotonic strategies and existence of ordinal mind change bound is also investigated.