Divide and Conquer Kernel Ridge Regression
نویسندگان
چکیده
We study a decomposition-based scalable approach to performing 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 main theorem establishes that despite the computational speed-up, statistical optimality is retained: if m is not too large, the partition-based estimate achieves optimal rates of convergence for the full sample size N . As concrete examples, our theory guarantees that m may grow polynomially in N for Sobolev spaces, and nearly linearly for finite-rank kernels and Gaussian kernels. We conclude with simulations complementing our theoretical results and exhibiting the computational and statistical benefits of our approach.
منابع مشابه
Divide and conquer kernel ridge regression: a distributed algorithm with minimax optimal rates
We study a decomposition-based scalable approach to kernel ridge regression, and show that it achieves minimax optimal convergence rates under relatively mild conditions. 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 using a careful choice of the regularization ...
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