|
| A Gradient Iteration Method for FunctionalLinear Regression in Reproducing KernelHilbert Spaces |
| Hongzhi Tong,Michael Ng |
| (School of Statistics, University of International Business and Economics,
Beijing 100029, China;Institute of Data Science and Department of Mathematics, The
University of Hong Kong, Pokfulam, Hong Kong, China) |
| DOI： |
| Abstract: |
| We consider a gradient iteration algorithm for prediction of functional linear regression under the framework of reproducing kernel Hilbert spaces.
In the algorithm, we use an early stopping technique, instead of the classical
Tikhonov regularization, to prevent the iteration from an overfitting function.
Under mild conditions, we obtain upper bounds, essentially matching the known
minimax lower bounds, for excess prediction risk. An almost sure convergence
is also established for the proposed algorithm. |
| Key words: Gradient iteration algorithm, functional linear regression, reproducing kernel
Hilbert space, early stopping, convergence rates. |