Tensor Decomposition via Variational Auto-Encoder

Abstract

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.