论文标题
非负张量的多体近似
Many-body Approximation for Non-negative Tensors
论文作者
论文摘要
我们提出了一种分解非负张量的替代方法，称为多体近似。传统的分解方法在表示中假设低级度，从而导致全球优化和目标排名选择的困难。我们通过张量的基于能量的建模来避免这些问题，其中张量及其模式分别对应于概率分布和随机变量。我们的模型可以通过将变量之间的相互作用（即模式）之间的相互作用（即，可以比等级更具直觉调谐）考虑在全球优化的情况下最小化。此外，我们将模式之间的相互作用视为张量网络，并揭示了多体近似和低级别近似之间的非平凡关系。我们证明了方法在张量完成和近似中的有效性。
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.
