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2013•Unpublished venueRequires access

A risk comparison of ordinary least squares vs ridge regression

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

Open publisher page 41 citations

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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What this paper is about

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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Available 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).

Key concepts: Ordinary least squares, Mathematics, Simple linear regression, Total least squares, Principal component regression, Generalized least squares, Least-squares function approximation, Subspace topology

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