A Risk Comparison of Ordinary Least Squares vs Ridge Regression

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

JMLR 2013 pp. 1505-1511

/jmlr/2013/dhillon2013jmlr-risk/

Abstract

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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Text

Dhillon et al. "A Risk Comparison of Ordinary Least Squares vs Ridge Regression." Journal of Machine Learning Research, 2013.

Markdown

[Dhillon et al. "A Risk Comparison of Ordinary Least Squares vs Ridge Regression." Journal of Machine Learning Research, 2013.](https://mlanthology.org/jmlr/2013/dhillon2013jmlr-risk/)

BibTeX

@article{dhillon2013jmlr-risk,
  title     = {{A Risk Comparison of Ordinary Least Squares vs Ridge Regression}},
  author    = {Dhillon, Paramveer S. and Foster, Dean P. and Kakade, Sham M. and Ungar, Lyle H.},
  journal   = {Journal of Machine Learning Research},
  year      = {2013},
  pages     = {1505-1511},
  volume    = {14},
  url       = {https://mlanthology.org/jmlr/2013/dhillon2013jmlr-risk/}
}