VSB-DVM: An end-to-end bayesian nonparametric generalization of deep variational mixture model

Mixture of factor analyzers is a fundamental model in unsupervised learning, which is particularly useful for high dimensional data. Recent efforts on deep auto-encoding mixture models made a fruitful progress in clustering. However, in most cases, their performance depends highly on the results of pre-training. Moreover, they tend to ignore the prior information when making clustering assignment, leading to a less strict inference and consequently limiting the performance. In this paper, we propose an end-to-end Bayesian nonparametric generalization of deep mixture model with a Variational Auto-Encoder (VAE) framework. Specifically, we develop a novel model called VSB-DVM exploiting the Variational Stick-Breaking Process to design a Deep Variational Mixture Model. Distinct from the existing deep auto-encoding mixture models, this novel unsupervised deep generative model can learn low-dimensional representations and clustering simultaneously without pre-training. Importantly, a strict inference is proposed using weights of stick-breaking process in a variational way. Furthermore, able to capture the richer statistical structure of the data, VSB-DVM can also generate highly realistic samples for any specified cluster. A series of experiments are carried out, both qualitatively and quantitatively, on benchmark clustering and generation tasks. Comparative results show that the proposed model is able to generate diverse and high-quality samples of data, and also achieves encouraging clustering results outperforming the state-of-the-art algorithms on four real-world datasets.