  We present a family of expectation-maximization (EM) algorithms for binary
and negative-binomial logistic regression, drawing a sharp connection with the
variational-Bayes algorithm of Jaakkola and Jordan (2000). Indeed, our results
allow a version of this variational-Bayes approach to be re-interpreted as a
true EM algorithm. We study several interesting features of the algorithm, and
of this previously unrecognized connection with variational Bayes. We also
generalize the approach to sparsity-promoting priors, and to an online method
whose convergence properties are easily established. This latter method
compares favorably with stochastic-gradient descent in situations with marked
collinearity.
