  We use the theory of normal variance-mean mixtures to derive a
data-augmentation scheme for a class of common regularization problems. This
generalizes existing theory on normal variance mixtures for priors in
regression and classification. It also allows variants of the
expectation-maximization algorithm to be brought to bear on a wider range of
models than previously appreciated. We demonstrate the method on several
examples, including sparse quantile regression and binary logistic regression.
We also show that quasi-Newton acceleration can substantially improve the speed
of the algorithm without compromising its robustness.
