Diversity-Promoting Bayesian Learning of Latent Variable Models

Abstract In learning latent variable models (LVMs), it is important to effectively capture infrequent patterns and shrink model size without sacrificing modeling power. Various studies have been done to "diversify" a LVM, which aim to learn a diverse set of latent components in LVMs. Most existing studies fall into a frequentist-style regularization framework, where the components are learned via point estimation. In this paper, we investigate how to "diversify" LVMs in the paradigm of Bayesian learning, which has advantages complementary to point estimation, such as alleviating overfitting via model averaging and quantifying uncertainty. We propose two approaches that have complementary advantages. One is to define diversity-promoting mutual angular priors which assign larger density to components with larger mutual angles based on Bayesian network and von Mises-Fisher distribution and use these priors to affect the posterior via Bayes rule. We develop two efficient approximate posterior inference algorithms based on variational inference and Markov chain Monte Carlo sampling. The other approach is to impose diversity-promoting regularization directly over the post-data distribution of components. These two methods are applied to the Bayesian mixture of experts model to encourage the "experts" to be diverse and experimental results demonstrate the effectiveness and efficiency of our methods