  Tensor train (TT) decomposition, a powerful tool for analyzing
multidimensional data, exhibits superior performance in many machine learning
tasks. However, existing methods for TT decomposition either suffer from noise
overfitting, or require extensive fine-tuning of the balance between model
complexity and representation accuracy. In this paper, a fully Bayesian
treatment of TT decomposition is employed to avoid noise overfitting, by
endowing it with the ability of automatic rank determination. In particular,
theoretical evidence is established for adopting a Gaussian-product-Gamma prior
to induce sparsity on the slices of the TT cores, so that the model complexity
is automatically determined even under incomplete and noisy observed data.
Furthermore, based on the proposed probabilistic model, an efficient learning
algorithm is derived under the variational inference framework. Simulation
results on synthetic data show the success of the proposed model and algorithm
in recovering the ground-truth TT structure from incomplete noisy data. Further
experiments on real-world data demonstrate the proposed algorithm performs
better in image completion and image classification, compared to other existing
TT decomposition algorithms.
