Distributed Generalized Cross-Validation for Divide-and-Conquer Kernel Ridge Regression and its Asymptotic Optimality
Year: 2016
Type: preprint
Abstract: Tuning parameter selection is of critical importance for kernel ridge regression. To this date, 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 data sets. In this paper, by modifying the Generalized Cross-validation (GCV, Wahba, 1990) 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 data sets, 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.
Source: arXiv (Cornell University)
Authors: Xu, Ganggang, Shang, Zuofeng, Cheng, Guang
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: Collaborative Research:Semiparametric ODE Models for Complex Gene Regulartory Networks, Collaborative Research: Nonparametric Bayesian Aggregation for Massive Data, G2821005409, G4353487559, CAREER: Bootstrap M-estimation in Semi-Nonparametric Models, G6671297155, Collaborative Research: Non- and Semi-Parametric Modeling of Structured Human Activity Patterns Using Point Processes, G7829600232, Collaborative Research: Nonparametric Bayesian Aggregation for Massive Data, G8876996369
OpenAlex ID: W2993407340