DeepAI AI Chat
Log In Sign Up

Divide and Conquer Kernel Ridge Regression: A Distributed Algorithm with Minimax Optimal Rates

by   Yuchen Zhang, et al.
berkeley college

We establish optimal convergence rates for a decomposition-based scalable approach to kernel ridge regression. The method is simple to describe: it randomly partitions a dataset of size N into m subsets of equal size, computes an independent kernel ridge regression estimator for each subset, then averages the local solutions into a global predictor. This partitioning leads to a substantial reduction in computation time versus the standard approach of performing kernel ridge regression on all N samples. Our two main theorems establish that despite the computational speed-up, statistical optimality is retained: as long as m is not too large, the partition-based estimator achieves the statistical minimax rate over all estimators using the set of N samples. As concrete examples, our theory guarantees that the number of processors m may grow nearly linearly for finite-rank kernels and Gaussian kernels and polynomially in N for Sobolev spaces, which in turn allows for substantial reductions in computational cost. We conclude with experiments on both simulated data and a music-prediction task that complement our theoretical results, exhibiting the computational and statistical benefits of our approach.


page 1

page 2

page 3

page 4


Kernel Ridge Regression via Partitioning

In this paper, we investigate a divide and conquer approach to Kernel Ri...

Parallelizing Spectral Algorithms for Kernel Learning

We consider a distributed learning approach in supervised learning for a...

Uncertainty quantification for distributed regression

The ever-growing size of the datasets renders well-studied learning tech...

Optimal Rates of Distributed Regression with Imperfect Kernels

Distributed machine learning systems have been receiving increasing atte...

Distributed Kernel Ridge Regression with Communications

This paper focuses on generalization performance analysis for distribute...

Distributed Learning with Dependent Samples

This paper focuses on learning rate analysis of distributed kernel ridge...

ParK: Sound and Efficient Kernel Ridge Regression by Feature Space Partitions

We introduce ParK, a new large-scale solver for kernel ridge regression....