An Iterative, Sketchingbased Framework for Ridge Regression
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Proceedings of the 35th International Conference on Machine Learning, PMLR 80:989998, 2018.
Abstract
Ridge regression is a variant of regularized least squares regression that is particularly suitable in settings where the number of predictor variables greatly exceeds the number of observations. We present a simple, iterative, sketchingbased algorithm for ridge regression that guarantees highquality approximations to the optimal solution vector. Our analysis builds upon two simple structural results that boil down to randomized matrix multiplication, a fundamental and wellunderstood primitive of randomized linear algebra. An important contribution of our work is the analysis of the behavior of subsampled ridge regression problems when the ridge leverage scores are used: we prove that accurate approximations can be achieved by a sample whose size depends on the degrees of freedom of the ridgeregression problem rather than the dimensions of the design matrix. Our experimental evaluations verify our theoretical results on both real and synthetic data.
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