Near-optimal Coresets For Least-Squares Regression

TL;DR

This paper develops deterministic polynomial-time algorithms to construct small, effective coresets for constrained and multiple response least-squares regression, providing near-optimal approximation guarantees.

Contribution

It introduces new deterministic algorithms for constructing coresets with provable approximation guarantees for various least-squares regression problems.

Findings

Algorithms achieve near-optimal approximation guarantees.

Lower bounds show limited room for improvement.

Applicable to constrained and multiple response regression.

Abstract

We study (constrained) least-squares regression as well as multiple response least-squares regression and ask the question of whether a subset of the data, a coreset, suffices to compute a good approximate solution to the regression. We give deterministic, low order polynomial-time algorithms to construct such coresets with approximation guarantees, together with lower bounds indicating that there is not much room for improvement upon our results.