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Title: Fridge: Focused fine-tuning of ridge regression for personalized predictions Authors:  Kristoffer Hellton - Norwegian Computing Center (Norway) [presenting]
Abstract: Penalized regression methods, depending on one or more tuning parameters, require fine-tuning to achieve optimal prediction performance. For ridge regression, there exist numerous approaches with cross-validation as the standard procedure, but common for all is that one single parameter is chosen for all future predictions. To better adapt to heterogeneity in high-dimensional data, we propose a focused ridge regression, the fridge procedure, with a unique tuning parameter for each covariate vector for which we wish to produce a prediction. The covariate vector specific tuning parameter is defined as the minimizer of the theoretical mean square prediction error, which is explicitly given in case of ridge regression. We propose to estimate the resulting tuning parameter through a plugin approach, and for high-dimensional data, ridge regression with cross-validation is used as the plugin estimate. The procedure is extended to logistic ridge regression by utilizing parametric bootstrap. Simulations show that fridge gives lower average prediction error than standard ridge regression in heterogeneous data, and we illustrate the method in an application of personalized medicine, predicting individual disease risk based on gene expression data.