  We present an expectation-maximization (EM) based unified framework for
non-negative tensor decomposition that optimizes the Kullback-Leibler
divergence. To avoid iterations in each M-step and learning rate tuning, we
establish a general relationship between low-rank decomposition and many-body
approximation. Using this connection, we exploit that the closed-form solution
of the many-body approximation can be used to update all parameters
simultaneously in the M-step. Our framework not only offers a unified
methodology for a variety of low-rank structures, including CP, Tucker, and
Train decompositions, but also their combinations forming mixtures of tensors
as well as robust adaptive noise modeling. Empirically, we demonstrate that our
framework provides superior generalization for discrete density estimation
compared to conventional tensor-based approaches.
