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.

基于期望最大化 (EM) 的非负张量分解统一框架，通过优化 Kullback-Leibler 散度来避免在每次 M 步骤和学习率调整中的迭代，并建立了低秩分解和多体逼近之间的一般关系，进而利用了多体逼近的闭式解来同时更新所有参数。我们的框架不仅为各种低秩结构（包括 CP、Tucker 和 Train 分解）提供了统一的方法，还包括了张量的组合形成混合以及稳健的自适应噪声建模。实证方面，与传统的基于张量的方法相比，我们的框架在离散密度估计方面提供了更好的泛化。