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

Document Type

Article

Publication Date

10-2-2019

Abstract

Tuning parameter selection is of critical importance for kernel ridge regression. To date, a data-driven tuning method for divide-and-conquer kernel ridge regression (d-KRR) has been lacking in the literature, which limits the applicability of d-KRR for large datasets. In this article, by modifying the generalized cross-validation (GCV) score, we propose a distributed generalized cross-validation (dGCV) as a data-driven tool for selecting the tuning parameters in d-KRR. Not only the proposed dGCV is computationally scalable for massive datasets, it is also shown, under mild conditions, to be asymptotically optimal in the sense that minimizing the dGCV score is equivalent to minimizing the true global conditional empirical loss of the averaged function estimator, extending the existing optimality results of GCV to the divide-and-conquer framework. Supplemental materials for this article are available online.

Identifier

85076878734 (Scopus)

Publication Title

Journal of Computational and Graphical Statistics

External Full Text Location

https://doi.org/10.1080/10618600.2019.1586714

e-ISSN

15372715

ISSN

10618600

First Page

891

Last Page

908

Issue

4

Volume

28

Grant

1811812

Fund Ref

Simons Foundation

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