A Risk Comparison of Ordinary Least Squares vs Ridge Regression

Paramveer S. Dhillon, Dean P. Foster, Sham M. Kakade, Lyle H. Ungar.

Year: 2013, Volume: 14, Issue: 46, Pages: 1505−1511


We compare the risk of ridge regression to a simple variant of ordinary least squares, in which one simply projects the data onto a finite dimensional subspace (as specified by a principal component analysis) and then performs an ordinary (un- regularized) least squares regression in this subspace. This note shows that the risk of this ordinary least squares method (PCA-OLS) is within a constant factor (namely 4) of the risk of ridge regression (RR).