Scalable Nonparametric Multiway Data Analysis

Multiway data analysis deals with multiway arrays, i.e., tensors, and the goal is twofold: predicting missing entries by modeling the interactions between array elements and discovering hidden patterns, such as clusters or communities in each mode. Despite the success of existing tensor factorization approaches, they are either unable to capture nonlinear interactions, or computationally expensive to handle massive data. In addition, most of the existing methods lack a principled way to discover latent clusters, which is important for better understanding of the data. To address these issues, we propose a scalable nonparametric tensor decomposition model. It employs Dirichlet process mixture (DPM) prior to model the latent clusters; it uses local Gaussian processes (GPs) to capture nonlinear relationships and to improve scalability. An efficient online variational Bayes Expectation-Maximization algorithm is proposed to learn the model. Experiments on both synthetic and real-world data show that the proposed model is able to discover latent clusters with higher prediction accuracy than competitive methods. Furthermore, the proposed model obtains significantly better predictive performance than the state-of-the-art large scale tensor decomposition algorithm, GigaTensor, on two large datasets with billions of entries.