  Existing Bayesian models, especially nonparametric Bayesian methods, rely on
specially conceived priors to incorporate domain knowledge for discovering
improved latent representations. While priors can affect posterior
distributions through Bayes' rule, imposing posterior regularization is
arguably more direct and in some cases more natural and general. In this paper,
we present regularized Bayesian inference (RegBayes), a novel computational
framework that performs posterior inference with a regularization term on the
desired post-data posterior distribution under an information theoretical
formulation. RegBayes is more flexible than the procedure that elicits expert
knowledge via priors, and it covers both directed Bayesian networks and
undirected Markov networks whose Bayesian formulation results in hybrid chain
graph models. When the regularization is induced from a linear operator on the
posterior distributions, such as the expectation operator, we present a general
convex-analysis theorem to characterize the solution of RegBayes. Furthermore,
we present two concrete examples of RegBayes, infinite latent support vector
machines (iLSVM) and multi-task infinite latent support vector machines
(MT-iLSVM), which explore the large-margin idea in combination with a
nonparametric Bayesian model for discovering predictive latent features for
classification and multi-task learning, respectively. We present efficient
inference methods and report empirical studies on several benchmark datasets,
which appear to demonstrate the merits inherited from both large-margin
learning and Bayesian nonparametrics. Such results were not available until
now, and contribute to push forward the interface between these two important
subfields, which have been largely treated as isolated in the community.
