Error analysis of regularized least-square regression with Fredholm kernel
This work addresses a theoretical gap in learning theory for researchers, though it appears incremental as it extends existing regression analysis to a specific kernel type.
The paper tackles the lack of generalization analysis for regularized least-square regression with Fredholm kernels by establishing a generalization bound, showing that a fast learning rate of O(l^{-1}) can be achieved under mild conditions, with simulated examples indicating satisfactory prediction performance.
Learning with Fredholm kernel has attracted increasing attention recently since it can effectively utilize the data information to improve the prediction performance. Despite rapid progress on theoretical and experimental evaluations, its generalization analysis has not been explored in learning theory literature. In this paper, we establish the generalization bound of least square regularized regression with Fredholm kernel, which implies that the fast learning rate O(l^{-1}) can be reached under mild capacity conditions. Simulated examples show that this Fredholm regression algorithm can achieve the satisfactory prediction performance.