  Tensor decomposition is an important technique for capturing the high-order
interactions among multiway data. Multi-linear tensor composition methods, such
as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the
complex interactions among objects are multi-linear, and are thus insufficient
to represent nonlinear relationships in data. Another assumption of these
methods is that a predefined rank should be known. However, the rank of tensors
is hard to estimate, especially for cases with missing values. To address these
issues, we design a Bayesian generative model for tensor decomposition.
Different from the traditional Bayesian methods, the high-order interactions of
tensor entries are modeled with variational auto-encoder. The proposed model
takes advantages of Neural Networks and nonparametric Bayesian models, by
replacing the multi-linear product in traditional Bayesian tensor decomposition
with a complex nonlinear function (via Neural Networks) whose parameters can be
learned from data. Experimental results on synthetic data and real-world
chemometrics tensor data have demonstrated that our new model can achieve
significantly higher prediction performance than the state-of-the-art tensor
decomposition approaches.
