Divide and Conquer Kernel Ridge Regression
published: Sept. 2, 2013, recorded: June 2013, views: 4134
Report a problem or upload filesIf you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
We study a decomposition-based scalable approach to performing kernel ridge regression. The method is simply described: 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: that so long as 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.
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !