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Rademacher and Gaussian Complexities: Risk Bounds and Structural Results
Open accessAbstract
We investigate the use of certain data-dependent estimates of the complexity of a function class, called Rademacher and Gaussian complexities. In a decision theoretic setting, we prove general risk bounds in terms of these complexities. We consider function classes that can be expressed as combinations of functions from basis classes and show how the Rademacher and Gaussian complexities of such a function class can be bounded in terms of the complexity of the basis classes. We give examples of the application of these techniques in finding data-dependent risk bounds for decision trees, neural networks and support vector machines.
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Cites
A Probabilistic Theory of Pattern Recognition
Devroye, L., Györfi, L., & Lugosi, G. (1996) · Stochastic Modelling and Applied Probability · doi:10.1007/978-1-4612-0711-5 · Cited by 3,274
On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
Vapnik, V. N., & Chervonenkis, A. Y. (1971) · Theory of Probability & Its Applications · doi:10.1137/1116025 · Cited by 2,448
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A Kernel Method for the Two-Sample-Problem
Gretton, A., Borgwardt, K. M., Rasch, M., Schölkopf, B., & Smola, A. J. (2007) · Advances in Neural Information Processing Systems 19 · doi:10.7551/mitpress/7503.003.0069 · Cited by 2,167
Metadata
- Authors
- Bartlett, P. L., & Mendelson, S.
- Venue
- Lecture Notes in Computer Science
- Publisher
- Springer Berlin Heidelberg
- Published
- 2001
- Pages
- 224-240
- ISSN
- 0302-9743 (ISSN-L)
- OpenAlex
- W2579923771
- Cited by
- 1,949
- References
- 2
- FWCI
- 9.83
- Type
- conference paper
- Language
- en
- Open access
- green
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