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 $L_1$ penalties. For ridge penalization using the

singular value decomposition we reduce the 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.