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Tuning parameter selection is of critical importance for kernel ridgeregression. To this date, data driven tuning method for divide-and-conquerkernel ridge regression (d-KRR) has been lacking in the literature, whichlimits the applicability of d-KRR for large data sets. In this paper, bymodifying the Generalized Cross-validation (GCV, Wahba, 1990) score, we proposea distributed Generalized Cross-Validation (dGCV) as a data-driven tool forselecting the tuning parameters in d-KRR. Not only the proposed dGCV iscomputationally scalable for massive data sets, it is also shown, under mildconditions, to be asymptotically optimal in the sense that minimizing the dGCVscore is equivalent to minimizing the true global conditional empirical loss ofthe averaged function estimator, extending the existing optimality results ofGCV to the divide-and-conquer framework.

Distributed Generalized Cross-Validation for Divide-and-Conquer Kernel Ridge Regression and its Asymptotic Optimality