Bayesian Factorizations of Big Sparse Tensors

摘要: It has become routine to collect data that are structured as multiway arrays (tensors). There is an enormous literature on low rank and sparse matrix factorizations, but limited consideration of extensions the tensor case in statistics. The most common factorization relies parallel factor analysis (PARAFAC), which expresses a k sum one tensors. In contingency table applications sample size massively less than number cells table, assumption not sufficient PARAFAC poor performance. We induce additional layer dimension reduction by allowing effective vary across dimensions table. Taking Bayesian approach, we place priors terms develop efficient Gibbs sampler for posterior computation. Theory provided showing concentration rates high-dimensional settings, methods shown have excellent performance simulations several ...