Algorithmic Learning Theory: 10th International Conference, by Katharina Morik (auth.), Osamu Watanabe, Takashi Yokomori

By Katharina Morik (auth.), Osamu Watanabe, Takashi Yokomori (eds.)

This e-book constitutes the refereed complaints of the tenth foreign convention on Algorithmic studying concept, ALT'99, held in Tokyo, Japan, in December 1999.
The 26 complete papers awarded have been rigorously reviewed and chosen from a complete of fifty one submissions. additionally incorporated are 3 invited papers. The papers are geared up in sections on studying size, Inductive Inference, Inductive common sense Programming, PAC studying, Mathematical instruments for studying, studying Recursive capabilities, question studying and online studying.

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Extra info for Algorithmic Learning Theory: 10th International Conference, ALT’99 Tokyo, Japan, December 6–8, 1999 Proceedings

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In order to make a connection between ESC and the minimax RCL, we focus on the specific case where H is a parametric class such that any prediction algorithm in H is written as a sequence of functions each of which belongs to a parametric class Hk = {fθ (·) : θ ∈ Θ} where Θ is a k-dimensional compact set in IRk . In this case the ESC of Dm relative to Hk is written as I(Dm : Hk ) = − 1 ln λ∗ ∗ dθπ(θ)e−λ m t=1 L(yy ,fθ (xt )) , (8) where π(θ) is a prior probability density over Θ. We make the following assumption for L, Hk , and π.

Extended Stochastic Complexity and Minimax Relative Loss Analysis 31 Lemma 1. Under Assumption 1, there exists a sequential prediction algorithm such that for any Dm , its cumulative loss is upper-bounded by I(Dm : H). Lemma 1 can be proven using Vovk’s aggregating algorithm [10] with its analysis in [3]. In order to make a connection between ESC and the minimax RCL, we focus on the specific case where H is a parametric class such that any prediction algorithm in H is written as a sequence of functions each of which belongs to a parametric class Hk = {fθ (·) : θ ∈ Θ} where Θ is a k-dimensional compact set in IRk .

29] Michael Kearns and Leslie G. Valiant. Learning Boolean formulae or finite automata is as hard as factoring. Technical Report TR-14-88, Harvard University Aiken Computation Laboratory, August 1988. [30] Michael Kearns and Leslie G. Valiant. Cryptographic limitations on learning Boolean formulae and finite automata. Journal of the Association for Computing Machinery, 41(1):67–95, January 1994. [31] Richard Maclin and David Opitz. An empirical evaluation of bagging and boosting. In Proceedings of the Fourteenth National Conference on Artificial Intelligence, pages 546–551, 1997.

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