Empirical Bayes Logistic Regression
We construct a diagnostic predictor for patient disease status based on a single data set of mass spectra of serum samples together with the binary case-control response. The model is logistic regression with Bernoulli log-likelihood augmented either by quadratic ridge or absolute L1 penalties. For ridge penalization using the singular value decomposition we reduce the number of variables for maximization to the rank of the design matrix. With log-likelihood loss, 10-fold cross-validatory choice is employed to specify the penalization hyperparameter. Predictive ability is judged on a set-aside subset of the data.
Foteini Strimenopoulou and Philip J. Brown. "Empirical Bayes Logistic Regression" Statistical Applications in Genetics and Molecular Biology 7.2 (2008).
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