  We present an alternative approach to decompose non-negative tensors, called
many-body approximation. Traditional decomposition methods assume low-rankness
in the representation, resulting in difficulties in global optimization and
target rank selection. We avoid these problems by energy-based modeling of
tensors, where a tensor and its mode correspond to a probability distribution
and a random variable, respectively. Our model can be globally optimized in
terms of the KL divergence minimization by taking the interaction between
variables (that is, modes), into account that can be tuned more intuitively
than ranks. Furthermore, we visualize interactions between modes as tensor
networks and reveal a nontrivial relationship between many-body approximation
and low-rank approximation. We demonstrate the effectiveness of our approach in
tensor completion and approximation.
