Bayesian Nonparametric Models for Multiway Data Analysis.

Tensor decomposition is a powerful computational tool for multiway data analysis. Many popular tensor decomposition approaches--such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)--amount to multi-linear factorization. They are insufficient to model (i) complex interactions between data entities, (ii) various data types (e.g.missing data and binary data), and (iii) noisy observations and outliers. To address these issues, we propose tensor-variate latent nonparametric Bayesian models, coupled with efficient inference methods, for multiway data analysis. We name these models InfTucker . Using these InfTucker models, we conduct Tucker decomposition in an infinite feature space. Unlike classical tensor decomposition models, our new approaches handle both continuous and binary data in a probabilistic framework. Unlike previous Bayesian models on matrices and tensors, our models are based on latent Gaussian or t processes with nonlinear covariance functions. Moreover, the proposed models can also be naturally applied in network modeling, which leads to powerful Bayesian nonparametric stochastic blockmodels. To efficiently learn the InfTucker models from data, we develop a variational inference technique on tensors. Compared with classical implementation, the new technique reduces both time and space complexities by several orders of magnitude. Experimental results on both multiway datasets and network data demonstrate the effectiveness of the proposed models.