Near-optimal Coresets For Least-Squares Regression
  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. 
Christos Boutsidis, Petros Drineas, Malik Magdon-Ismail
cs.DS cs.LG