Randomized Sketching for Large-Scale Sparse Ridge Regression Problems

Abstract

We present a fast randomized ridge regression solver for sparse overdetermined matrices in distributed-memory platforms. Our solver is based on the Blendenpik algorithm, but employs sparse random projection schemes to construct a sketch of the input matrix. These sparse random projection sketching schemes, and in particular the use of the Randomized Sparsity-Preserving Transform, enable our algorithm to scale the distributed memory vanilla implementation of Blendenpik and provide up to × 13 speedup over a state-of-the-art parallel Cholesky-like sparse-direct solver.