By Hans Ulrich Simon (auth.), David Helmbold, Bob Williamson (eds.)
This booklet constitutes the refereed complaints of the 14th Annual and fifth ecu meetings on Computational studying conception, COLT/EuroCOLT 2001, held in Amsterdam, The Netherlands, in July 2001.
The forty revised complete papers offered including one invited paper have been rigorously reviewed and chosen from a complete of sixty nine submissions. All present elements of computational studying and its purposes in a number of fields are addressed.
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Additional info for Computational Learning Theory: 14th Annual Conference on Computational Learning Theory, COLT 2001 and 5th European Conference on Computational Learning Theory, EuroCOLT 2001 Amsterdam, The Netherlands, July 16–19, 2001 Proceedings
Layered neural networks with Gaussian hidden units as universal approximations. Neural Computation, 2:210–215, 1990. 10. Pascal Koiran and Eduardo D. Sontag. Neural networks with quadratic VC dimension. Journal of Computer and System Sciences, 54:190–198, 1997. 30 M. Schmitt 11. Wee Sun Lee, Peter L. Bartlett, and Robert C. Williamson. Lower bounds on the VC dimension of smoothly parameterized function classes. Neural Computation, 7:1040–1053, 1995. 12. Wee Sun Lee, Peter L. Bartlett, and Robert C.
1) i=1 For example, with the prediction function pred(v, x) = v · x the quadratic loss Lsq (y, yˆ) = (y − yˆ)2 satisﬁes1 (1) with (c, η) = (2, 12 ) and the entropic loss Lent (y, yˆ) = y ln yyˆ + (1 − y) ln 1−y 1−ˆ y satisﬁes (1) with (c, η) = (1, 1). In the remainder we will assume the loss and prediction functions that we use are (c, 1/c)-realizable so that cη = 1. The two examples given above satisfy this criterion. This does not include the case of the absolute loss. However, the results here can essentially be extended to this loss as was done in .
K. Warmuth prove lower bounds on the loss of any on-line algorithm in terms of the number of bits needed to encode the partition. Acknowledgments The authors are grateful to Yoav Freund and Mark Herbster for many inspiring discussions. References 1. P. Auer, N. Cesa-Bianchi, and C. Gentile. Adaptive and self-conﬁdent on-line learning algorithms. NeuroCOLT Technical Report NC-TR-00-083, 2000. An extended abstract appeared in Proc. 13th Ann. Conf. Computational Learning Theory. 2. P. Auer and M. K.