Faster Ridge Regression via the Subsampled Randomized Hadamard Transform

We propose a fast algorithm for ridge regression when the number of features is much larger than the number of observations (p≫n). The standard way to solve ridge regression in this setting works in the dual space and gives a running time of O(n2p). Our algorithm Subsampled Randomized Hadamard Transform - Dual Ridge Regression (SRHT-DRR) runs in time O(np log(n)) and works by preconditioning the design matrix by a Randomized Walsh-Hadamard Transform with a subsequent subsampling of features. We provide risk bounds for our SRHT-DRR algorithm in the fixed design setting and show experimental results on synthetic and real datasets.