Abstract

Divide-and-conquer is a powerful approach for large and massive data analysis. In the nonparameteric regression setting, although various theore ical frameworks have been established to achieve optimality in estimation or hypothesis testing, how to choose the tuning parameter in a practically effective way is still an open problem. In t paper, we propose a data-driven procedure based on divide-and-conquer for selecting the tuning parameters in kernel ridge regression by modifying the popular Generalized Cross-validation (GCV, Wahba, 1990). While the proposed criterion is computationally scalable for massive data sets, it is also shown under mild conditions to be asymptotically optimal in the sense that minimizing the proposed distributed-GCV (dGCV) criterion is equivalent to minimizing the true global conditional empirical loss of the averaged function est mator, extending the existing optimality results o GCV to the divide-and-conquer framework.