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.

翻译：我们提出了一种基于期望最大化（EM）的统一框架，用于优化Kullback-Leibler散度的非负张量分解。为避免每个M步中的迭代以及学习率调优，我们建立了低秩分解与多体近似之间的通用关系。利用这一关联，我们提出多体近似的闭式解可用于在M步中同时更新所有参数。我们的框架不仅为多种低秩结构（包括CP、Tucker和Train分解）提供了统一方法，还支持这些结构组合形成的张量混合以及鲁棒自适应噪声建模。实证表明，与传统基于张量的方法相比，我们的框架在离散密度估计任务中展现出更优越的泛化性能。