Read e-book online Algorithmic Learning Theory: 14th International Conference, PDF

By Thomas Eiter (auth.), Ricard Gavaldá, Klaus P. Jantke, Eiji Takimoto (eds.)

ISBN-10: 3540202919

ISBN-13: 9783540202912

This ebook constitutes the refereed lawsuits of the 14th foreign convention on Algorithmic studying conception, ALT 2003, held in Sapporo, Japan in October 2003.

The 19 revised complete papers awarded including 2 invited papers and abstracts of three invited talks have been rigorously reviewed and chosen from 37 submissions. The papers are prepared in topical sections on inductive inference, studying and data extraction, studying with queries, studying with non-linear optimization, studying from random examples, and on-line prediction.

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Additional info for Algorithmic Learning Theory: 14th International Conference, ALT 2003, Sapporo, Japan, October 17-19, 2003. Proceedings

Sample text

If δ, f are finite, Θ(δ, f ) = (γ, g), one can effectively (in δ, f ) enumerate γ, g. This finally allows for the following definition of UEx -reducibility. Definition 10 Let D1 , D2 ∈ UEx . Fix a recursive meta-operator Θ and a recursive operator Ξ. D1 is UEx -reducible to D2 via Θ and Ξ, iff for any d1 ∈ D1 , any f1 ∈ Rd1 , and any initial segment δ1 there are functions δ2 and f2 satisfying: 1. Θ(δ1 d∞ 1 , f1 ) = (δ2 , f2 ), 2. δ2 converges to some description d2 ∈ D2 such that f2 ∈ Rd2 , 3. if σ is admissible for f2 , then Ξ(σ) is admissible for f1 .

Assume D to be a class of admissible probability distributions over A+ such that α ≥ α∗ , β ≤ β∗ and E[Λ] finite for all distributions D ∈ D . Then (PAT , D) is stochastically finitely learnable with high confidence from text. Proof. Let D ∈ D , and let δ ∈ (0, 1) be arbitrarily fixed. Furthermore, let t = s1 , s2 , s3 , . . be any randomly generated text with respect to D for the target pattern language. The wanted learner M uses the LWA as a subroutine. Additionally, it has a counter for memorizing the number of examples already seen.

If the target pattern does not contain any variable then the LWA converges after having read the first example. , the target pattern has to contain at least one variable. Our next theorem analyzes the complexity of the union operation. Theorem 7 (Rossmanith and Zeugmann [36]). The union operation can be computed in linear time. Furthermore, the following bound for the stage of convergence for every target pattern from Pat k can be shown. Theorem 8 (Rossmanith and Zeugmann [36]). 1 E[CONV ] = O · log1/β (k) for all k ≥ 2 .

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Algorithmic Learning Theory: 14th International Conference, ALT 2003, Sapporo, Japan, October 17-19, 2003. Proceedings by Thomas Eiter (auth.), Ricard Gavaldá, Klaus P. Jantke, Eiji Takimoto (eds.)


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