无界抽样情形下不定核的系数正则化回归
摘要
We investigate the coefficient-based regularized least squares regression with unbounded sampling in a data dependent hypothesis space. The learning scheme is essentially different from the standard one in a reproducing kernel Hilbert space: we do not need the kernel to be symmetric or positive semi-definite except for continuity and boundedness, the regularizer is the <italic>l</italic><sup>2</sup>-norm of a function expansion involving samples and the unboudedness of the sampling output. This leads to additional difficulty in the error analysis. In this paper, the goal is to investigate some concentration estimates for the error based on <italic>l</italic><sup>2</sup>-empirical covering numbers without the assumption of uniform boundedness for sampling. By introducing a suitable reproducing kernel Hilbert space and applying concentration techniques with <italic>l</italic><sup>2</sup>-empirical covering numbers, we derive satisfactory learning rates in terms of regularity of the regression function and capacity of the hypothesis space.