Coefficient regularized regression with non-iid sampling

Abstract

In this paper, we study a more general kernel regression learning with coefficient regularization. A non-iid setting is considered, where the sequence of probability measures for sampling is not identical but the sequence of marginal distributions for sampling converges exponentially fast in the dual of a Holder space; the sampling z _i , i ≥ 1 are weakly dependent, which satisfy a strongly mixing condition. Satisfactory capacity independently error bounds and learning rates are derived by the techniques of integral operator for this learning algorithm.

Keywords:

• learning theory
• coefficient regularized regression
• strong mixing condition
• approximation error
• sample error

2000 AMS Subject Classifications :

• 68T05
• 68Q32
• 62J02

Acknowledgements

The work described in this paper is supported by the Natural Science Foundation of China (Grant no. 11071276) and the Nature Science Fund of Shandong Province, China (Grant no. Y2007A11).