A risk comparison of ordinary least squares vs ridge regression

@article{Dhillon2013ARC,
  title={A risk comparison of ordinary least squares vs ridge regression},
  author={Paramveer S. Dhillon and Dean P. Foster and Sham M. Kakade and Lyle H. Ungar},
  journal={Journal of Machine Learning Research},
  year={2013},
  volume={14},
  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). 
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