Download Algorithmic Learning Theory: 19th International Conference, by Imre Csiszár (auth.), Yoav Freund, László Györfi, György PDF

By Imre Csiszár (auth.), Yoav Freund, László Györfi, György Turán, Thomas Zeugmann (eds.)

This booklet constitutes the refereed court cases of the nineteenth foreign convention on Algorithmic studying concept, ALT 2008, held in Budapest, Hungary, in October 2008, co-located with the eleventh foreign convention on Discovery technological know-how, DS 2008.

The 31 revised complete papers offered including the abstracts of five invited talks have been conscientiously reviewed and chosen from forty six submissions. The papers are devoted to the theoretical foundations of computer studying; they deal with issues corresponding to statistical studying; likelihood and stochastic methods; boosting and specialists; energetic and question studying; and inductive inference.

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Extra info for Algorithmic Learning Theory: 19th International Conference, ALT 2008, Budapest, Hungary, October 13-16, 2008. Proceedings

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D − 1 and for k = 0, . . ) Set the entropy measure: ˆ − (βd,k+1 − βd,k )α(C). ˆ Λd,k+1 (C) = (αd,k+1 − αd,k )β(C) Find the best subset Cd+1,2k of rectangle Cd,k in the AUC sense: Cd+1,2k = arg max Λd,k+1 (C) . C∈C, C⊂Cd,k Then, set Cd+1,2k+1 = Cd,k \ Cd+1,2k . ) Set ˆ d+1,2k ) ˆ (Cd+1,2k ) and βd+1,2k+1 = βd,k + β(C αd+1,2k+1 = αd,k + α as well as αd+1,2k+2 = αd,k+1 and βd+1,2k+2 = βd,k+1 . 3. Output. After D iterations, get the piecewise constant scoring function: 2D −1 (2D − k) I{x ∈ CD,k } sD (x) = k=0 The main features of the TreeRank algorithm are listed in the following remarks.

Section 2 describes in detail the sample selection bias correction technique. Section 3 introduces the concept of distributional stability and proves the distributional stability of kernel-based regularization algorithms. Section 4 analyzes the effect of estimation error using distributionally stable algorithms for both the clusterbased and the KMM estimation techniques. Section 5 reports the results of experiments with several data sets comparing these estimation techniques. 1 Sample Selection Bias Correction Problem Let X denote the input space and Y the label set, which may be {0, 1} in classification or any measurable subset of R in regression estimation problems, and let D denote the true distribution over X × Y according to which test points are drawn.

This is in fact a technique commonly used in statistics and machine learning for Y. Freund et al. ): ALT 2008, LNAI 5254, pp. 38–53, 2008. c Springer-Verlag Berlin Heidelberg 2008 Sample Selection Bias Correction Theory 39 a variety of problems of this type (Little & Rubin, 1986). With the exact weights, this reweighting could optimally correct the bias, but, in practice, the weights are based on an estimate of the sampling probability from finite data sets. Thus, it is important to determine to what extent the error in this estimation can affect the accuracy of the hypothesis returned by the learning algorithm.

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