  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, 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. To efficiently
learn the InfTucker 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. Our experimental
results on chemometrics and social network datasets demonstrate that our new
models achieved significantly higher prediction accuracy than the most
state-of-art tensor decomposition
