Bayesian Inference with Posterior Regularization and Infinite Latent SVMs

Existing Bayesian models, especially nonparametric Bayesian methods, rely heavily on specially conceived priors to incorporate domain knowledge for discovering improved latent representations. While priors can affect posterior distributions through Bayes' theorem, imposing posterior regularization is arguably more direct and in some cases can be more natural and easier. In this paper, we present regularized Bayesian inference (RegBayes), a computational framework to perform posterior inference with a convex regularization on the desired post-data posterior distributions. RegBayes covers both directed Bayesian networks and undirected Markov networks whose Bayesian formulation results in hybrid chain graph models. When the convex regularization is induced from a linear operator on the posterior distributions, RegBayes can be solved with convex analysis theory. 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.