Computational Learning Theory: 4th European Conference, by Robert E. Schapire (auth.), Paul Fischer, Hans Ulrich Simon

By Robert E. Schapire (auth.), Paul Fischer, Hans Ulrich Simon (eds.)

This booklet constitutes the refereed complaints of the 4th eu convention on Computational studying conception, EuroCOLT'99, held in Nordkirchen, Germany in March 1999. The 21 revised complete papers offered have been chosen from a complete of 35 submissions; additionally integrated are invited contributions. The ebook is split in topical sections on studying from queries and counterexamples, reinforcement studying, on-line studying and export recommendation, instructing and studying, inductive inference, and statistical conception of studying and trend reputation.

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Extra info for Computational Learning Theory: 4th European Conference, EuroCOLT’99 Nordkirchen, Germany, March 29–31, 1999 Proceedings

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On the other hand, the methods outlined in the previous section and section 5 can be used to handle gradients with negative components. The approach used by R¨ atsch et al. [13] can similarly be interpreted as a potential function of the margins. Recently, Friedman et al. [8] have given a maximum likelihood motivation for AdaBoost, and introduced another leveraging algorithm based on the log-likelihood criteria. They indicate that minimizing the square loss potential, (H − 1)2 performed less well in experiments than other monotone potentials, and conjecture that its non-monotonicity (penalizing margins greater than 1) is a contributing factor.

We define bad pair to be a pair of hypotheses from the version space that differ on more then proportion α of the samples. e. if two hypotheses are picked independently from the version space, the probability that they form a bad pair is less then β4k . We will show that if the algorithm did not make a query for tk consecutive samples, then the probability that the queries sampled do not form an α − β4k -net, is bounded by βk /4. Let W = {(h1 , h2 ) |Prx [h1 (x) = h2 (x)] ≥ α}. We would like to bound the probability that Pr[W ] > βk /4 when QBC” didn’t query for a tag for tk at the last consecutive samples: If Pr[W ] > βk /4, then the probability that the QBC algorithm will query for a tag is greater then αβk /4.

Learning Theory, pages 277–289, San Mateo, CA, 1991. Morgan Kaufmann. 2. B. E. Boser, I. M. Guyon, and V. N. Vapnik. A training algorithm for optimal margin classifiers. In Proc. 5th Annu. Workshop on Comput. Learning Theory, pages 144–152. ACM Press, New York, NY, 1992. 3. Leo Breiman. Bagging predictors. Machine Learning, 24(2):123–140, 1996. 4. Leo Breiman. Arcing the edge. Technical Report 486, Department of Statistics, University of California, Berkeley, 1997. edu. 5. Leo Breiman. Bias, variance, and arcing classifiers.

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