Abstract
We study the sample complexity of proper and improper learning problems with respect to different L q loss functions. We improve the known estimates for classes which have relatively small covering numbers (log-covering numbers which are polynomial with exponent p < 2) with respect to the L q norm for q = 2.
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References
M. Anthony, P.L. Bartlett: Neural Network Learning: Theoretical Foundations, Cambridge University Press, 1999.
B. Beauzamy: Introduction to Banach spaces and their Geometry, Math. Studies, vol 86, North-Holland, 1982
O. Hanner: On the uniform convexity of L p and l p, Ark. Math. 3, 239–244, 1956.
P. Habala, P. Haĵek, V. Zizler: Introduction to Banach spaces vol I and II, matfyzpress, Univ. Karlovy, Prague, 1996.
W.S. Lee: Agnostic learning and single hidden layer neural network, Ph.D. thesis, The Australian National University, 1996.
W.S. Lee, P.L. Bartlett, R.C. Williamson: The Importance of Convexity in Learning with SquaredLoss, IEEE Transactions on Information Theory 445, 1974–1980, 1998.
S. Mendelson: Rademacher averages and phase transitions in Glivenko-Cantelli classes, preprint.
S. Mendelson: Geometric methods in the analysis of Glivenko-Cantelli classes, this volume.
M. Talagrand: Sharper bounds for Gaussian and empirical processes, Annals of Probability, 22(1), 28–76, 1994.
A.W. Van-der-Vaart, J.A. Wellner: Weak convergence and Empirical Processes, Springer-Verlag, 1996.
R.C. Williamson, A.J. Smola, B. Schölkopf: Generalization performance of regularization networks andsupp ort vectors machines via entropy numbers of compact operators, to appear in IEEE transactions on Information Theory.
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© 2001 Springer-Verlag Berlin Heidelberg
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Mendelson, S. (2001). Learning Relatively Small Classes. In: Helmbold, D., Williamson, B. (eds) Computational Learning Theory. COLT 2001. Lecture Notes in Computer Science(), vol 2111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44581-1_18
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DOI: https://doi.org/10.1007/3-540-44581-1_18
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