Abstract: Algorithms for decompositions of matrices and tensors are of central importance in machine learning, signal processing and information retrieval. In recent years tensor methods, that compute decompositions of multidimensional arrays have gained significant popularity. Notable extensions include coupled factorizations where multiple observed tensors are factorized collectively; such methods are in particular useful for information fusion. We will discuss a subset of such tensor models from a statistical modeling perspective, building upon probabilistic generative models and generalized linear models.Probabilistic interpretations of factorization models facilitate the construction of application specific models. Here, the factorization is implicit in a well-defined statistical model and factorizations can be computed via maximum likelihood. Full Bayesian inference and model selection are also feasible via variational approximations or Markov Chain Monte Carlo methods.