کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4605287 | 1337560 | 2011 | 17 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Concentration estimates for learning with ℓ1-regularizer and data dependent hypothesis spaces Concentration estimates for learning with ℓ1-regularizer and data dependent hypothesis spaces](/preview/png/4605287.png)
We consider the regression problem by learning with a regularization scheme in a data dependent hypothesis space and ℓ1-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 ℓ1-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 ℓ2-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 ℓ1-regularizer and non-symmetric kernel has nice behaviors in terms of the ℓ2-empirical covering numbers of its unit ball.
Journal: Applied and Computational Harmonic Analysis - Volume 31, Issue 2, September 2011, Pages 286-302