By Imre Csiszár (auth.), Yoav Freund, László Györfi, György Turán, Thomas Zeugmann (eds.)
This ebook constitutes the refereed court cases of the nineteenth overseas convention on Algorithmic studying concept, ALT 2008, held in Budapest, Hungary, in October 2008, co-located with the eleventh foreign convention on Discovery technology, DS 2008.
The 31 revised complete papers awarded 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 computing device studying; they handle subject matters reminiscent of statistical studying; likelihood and stochastic strategies; boosting and specialists; lively and question studying; and inductive inference.
Read Online or Download Algorithmic Learning Theory: 19th International Conference, ALT 2008, Budapest, Hungary, October 13-16, 2008. Proceedings PDF
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Extra info for Algorithmic Learning Theory: 19th International Conference, ALT 2008, Budapest, Hungary, October 13-16, 2008. Proceedings
However, since Pr[s = 1] is a constant independent of x, its estimation is not even necessary. If the estimation of the sampling probability Pr[s = 1|x] from the unlabeled data set U were exact, then the reweighting just discussed could correct the sample bias optimally. Several techniques have been commonly used to estimate the reweighting quantities. But, these estimate weights are not guaranteed to be exact. The next section addresses how the error in that estimation aﬀects the error rate of the hypothesis returned by the learning algorithm.
Let F be a class of real-valued functions on X, and let A be an ordinal regression algorithm which, given as input a training sample S ∈ (X × [r])m , learns a real-valued function fS ∈ F and a threshold vector bS ∈ [−B, B]r−1 , and returns as output the prediction rule gS ≡ gfS ,bS . Let γ > 0. Then for any 0 < δ < 1 and for any distribution D on X × [r], with probability at least 1 − δ over the draw of S (according to Dm ), γ Lord D (gS ) ≤ LS (fS , bS ) + (r − 1) where LγS denotes the empirical 8 m γ -error, ln N∞ (γ/2, F , 2m) + ln 4B(r − 1) δγ and N∞ refers to d∞ covering numbers.
2d−1 − 1}, ∗ ∗ ) − α(Cd,2k )| + |β(Cd,2k ) − β(Cd,2k )| ≤ κd2 B(d + 1, n, δ), |α(Cd,2k where: ∀(d, n, δ) ∈ N × N×]0, 1[, B(d, n, δ) = c21 V n 1 2d + c22 log(1/δ) n 1 2d . Sample Selection Bias Correction Theory Corinna Cortes1 , Mehryar Mohri1,2 , Michael Riley1 , and Afshin Rostamizadeh2 2 1 Google Research, 76 Ninth Avenue, New York, NY 10011 Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012 Abstract. This paper presents a theoretical analysis of sample selection bias correction.