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• W2186535648 abstract "Ridge regression provides coefficient estimates via shrinkage, even when the observed design matrix contains correlated covariates, or when it is singular, as when the number of covariates exceeds the number of observations. This shrinking usually improve predictions in the linear model, compared to ordinary least-squares. However, the estimation and prediction accuracy of the ridge model depend on the choice of the ridge parameter. The current approaches to estimating the ridge parameter are based on minimizing cross-validation or information loss criteria, which are either computationally expensive or asymptotically inconsistent, and can only approximate (−2 times the log-) marginal likelihood of the model parameters. The marginal likelihood depends on a matrix determinant, which is computationally demanding when the number of covariates is large. This paper shows that after taking a singular value decomposition of the design matrix, the marginal likelihood can be simplified into an equation involving no matrix operations such as determinants or inverses. This simplification allows for a fast estimation of the ridge parameter based on a simple optimization algorithm, which typically completes in less than one-tenth of a second, even for data sets where the number of covariates and/or sample size is very large. Also, the marginal likelihood estimate of the ridge parameter is the “Bayes empirical Bayes” posterior mode, and is preferred according to the Bayes factor, over pair-wise comparisons of all possible ridge parameter estimates. We illustrate the speed and viability of the ridge parameter estimation method through the analysis of several real data sets, involving hundreds to several thousand covariates and observations, and involving more covariates than" @default.
• W2186535648 created "2016-06-24" @default.
• W2186535648 creator A5082741454 @default.
• W2186535648 date "2015-01-01" @default.
• W2186535648 modified "2023-09-27" @default.
• W2186535648 title "Fast Marginal Likelihood Estimation of the Ridge Parameter in Ridge Regression" @default.
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