Exponential family tensor factorization: an online extension and applications

In this paper, we propose a new probabilistic model of heterogeneously attributed multi-dimensional arrays. The model can manage heterogeneity by employing individual exponential family distributions for each attribute of the tensor array. Entries of the tensor are connected by latent variables and share information across the different attributes through the latent variables. The assumption of heterogeneity makes a Bayesian inference intractable, and we cast the EM algorithm approximated by the Laplace method and Gaussian process. We also extended the proposal algorithm for online learning. We apply our method to missing-values prediction and anomaly detection problems and show that our method outperforms conventional approaches that do not consider heterogeneity.