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

arXiv: https://arxiv.org/abs/1612.05907 · HTML: https://mlsanity.com/paper/1612.05907/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2016.

## Built on by (most cited first, 9 of 9)

- [Risk and cross validation in ridge regression with correlated samples](https://mlsanity.com/paper/2408.04607/) (2024)
- [Data splitting improves statistical performance in overparametrized regimes](https://mlsanity.com/paper/2110.10956/) (2021)
- [ROTI-GCV: Generalized Cross-Validation for right-ROTationally Invariant Data](https://mlsanity.com/paper/2406.11666/) (2024)
- [Asynchronous and Distributed Data Augmentation for Massive Data Settings](https://mlsanity.com/paper/2109.08969/) (2021)
- [Locally Adaptive and Differentiable Regression](https://mlsanity.com/paper/2308.07418/) (2023)
- [Adaptive Distributed Kernel Ridge Regression: A Feasible Distributed Learning Scheme for Data Silos](https://mlsanity.com/paper/2309.04236/) (2023)
- [Distributed Adaptive Nearest Neighbor Classifier: Algorithm and Theory](https://mlsanity.com/paper/2105.09788/) (2021)
- [Oversampling Divide-and-conquer for Response-skewed Kernel Ridge Regression](https://mlsanity.com/paper/2107.05834/) (2021)
- [Local SGD in Overparameterized Linear Regression](https://mlsanity.com/paper/2210.11562/) (2022)

## Abstract (arXiv)

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.