ridge

Ridge Regression. When the predictor variables are highly correlated amongst themselves, the coefficients of the resulting least squares fit may be very imprecise. By allowing a small amount of bias in the estimates, more reasonable coefficients may often be obtained. Ridge regression is one method to address these issues. Often, small amounts of bias lead to dramatic reductions in the variance of the estimated model coefficients. Ridge regression is such a technique which shrinks the regression coefficients by imposing a penalty on their size. Ridge regression was originally developed to overcome the singularity of the X'X matrix. This matrix is perturbed so as to make its determinant appreciably different from 0.

Ridge regression is a kind of Tikhonov regularization, which is the most commonly used method of regularization of ill-posed problems. Another interpretation of ridge regression is available through Bayesian estimation. In this setting the belief that weight should be small is coded into a prior distribution.

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