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Concentration estimates for learning with -regularizer and data dependent hypothesis spaces
- Source :
-
Applied & Computational Harmonic Analysis . Sep2011, Vol. 31 Issue 2, p286-302. 17p. - Publication Year :
- 2011
-
Abstract
- Abstract: We consider the regression problem by learning with a regularization scheme in a data dependent hypothesis space and -regularizer. The data dependence nature of the kernel-based hypothesis space provides flexibility for the learning algorithm. The regularization scheme is essentially different from the standard one in a reproducing kernel Hilbert space: the kernel is not necessarily symmetric or positive semi-definite and the regularizer is the -norm of a function expansion involving samples. The differences lead to additional difficulty in the error analysis. In this paper we apply concentration techniques with -empirical covering numbers to improve the learning rates for the algorithm. Sparsity of the algorithm is studied based on our error analysis. We also show that a function space involved in the error analysis induced by the -regularizer and non-symmetric kernel has nice behaviors in terms of the -empirical covering numbers of its unit ball. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 10635203
- Volume :
- 31
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Applied & Computational Harmonic Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 61243694
- Full Text :
- https://doi.org/10.1016/j.acha.2011.01.001