Half supervised coefficient regularization for regression learning with unbounded sampling

Abstract

In this study, we investigate the consistency of half supervised coefficient regularization learning with indefinite kernels. In our setting, the hypothesis space and learning algorithms are based on two different groups of input data which are drawn i.i.d. according to an unknown probability measure ρ _X . The only conditions imposed on the kernel function are the continuity and boundedness instead of a Mercer kernel and the output data are not asked to be bounded uniformly. By a mild assumption of unbounded output data and a refined integral operator technique, the generalization error is decomposed into hypothesis error, sample error and approximation error. By estimating these three parts, we deduce satisfactory learning rates with proper choice of the regularization parameter.

Keywords:

• unbounded hypothesis
• indefinite kernel
• coefficient regularization
• least square regression
• error bound
• learning rate

2010 AMS Subject Classifications:

• 68T05
• 62J02

Acknowledgements

This work was supported by the National Nature Science Foundation of China (No. 11071276).