Bayesian Multi-view Tensor Factorization

We introduce a Bayesian extension of the tensor factorization problem to multiple coupled tensors. For a single tensor it reduces to standard PARAFAC-type Bayesian factorization, and for two tensors it is the first Bayesian Tensor Canonical Correlation Analysis method. It can also be seen to solve a tensorial extension of the recent Group Factor Analysis problem. The method decomposes the set of tensors to factors shared by subsets of the tensors, and factors private to individual tensors, and does not assume orthogonality. For a single tensor, the method empirically outperforms existing methods, and we demonstrate its performance on multiple tensor factorization tasks in toxicogenomics and functional neuroimaging.