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.

翻译：我们提出了一种分解非负张量的新方法，称为多体近似。传统分解方法假设表示具有低秩性，因而在全局优化和目标秩选取方面存在困难。通过基于能量的张量建模，我们避免了这些问题。在该模型中，张量及其模式分别对应于概率分布和随机变量。通过考虑变量（即模式）间的交互作用（其可调性比秩更直观），我们的模型能够在KL散度最小化框架下实现全局优化。此外，我们将模式间的交互作用可视化为张量网络，并揭示出多体近似与低秩近似之间非平凡的关系。我们通过在张量补全与近似任务中的实验证明了该方法的有效性。