Many-body Approximation for Non-negative Tensors

Kazu Ghalamkari, Mahito Sugiyama, Yoshinobu Kawahara

Keywords: Tensor decomposition, Energy based model, Tensor networks

TL;DR: We formulate rank-free tensor decomposition via energy-based modeling of interactions between tensor modes. We analyze the relationship between our model and existing low-rank approximation models using tensor networks.

Abstract: 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.

Submission Number: 3907