Hierarchical Dirichlet Scaling Process

We present the hierarchical Dirichlet scal-ing process (HDSP), a Bayesian nonparametric mixed membership model for multi-labeled data. We construct the HDSP based on the gamma rep-resentation of the hierarchical Dirichlet process (HDP) which allows scaling the mixture com-ponents. With such construction, HDSP allo-cates a latent location to each label and mixture component in a space, and uses the distance be-tween them to guide membership probabilities. We develop a variational Bayes algorithm for the approximate posterior inference of the HDSP. Through experiments on synthetic datasets as well as datasets of newswire, medical journal ar-ticles, and Wikipedia, we show that the HDSP re-sults in better predictive performance than HDP, labeled LDA and partially labeled LDA. 1