标题： 超越独立成分分析：可识别性和算法 显示英文标题

标题： Beyond independent component analysis: identifiability and algorithms

摘要： 独立成分分析（ICA）是一种经典的恢复具有有用可识别性质的潜在变量的方法。 对于独立变量，累积张量是对角的；放松独立性会得到零结构推广对角性的张量。 这些模型已成为非独立成分分析近期研究的主题。 我们表明，成对均值独立性回答了可以放松独立性多少的问题：它是可识别的，任何更弱的概念都是不可识别的，并且它包含了之前研究的模型作为特例。 我们的结果适用于在任何累积张量上具有所需零模式分布的情况。 我们提出了一种基于正交群上的最小二乘优化的代数恢复算法。 模拟结果突出了稳健性：强制完全独立性可能会损害估计，而成对均值独立性则能实现更稳定的恢复。 这些发现扩展了经典的ICA框架，并为超越独立性的盲源分离提供了严格的理论基础。 显示英文摘要

摘要： Independent Component Analysis (ICA) is a classical method for recovering latent variables with useful identifiability properties. For independent variables, cumulant tensors are diagonal; relaxing independence yields tensors whose zero structure generalizes diagonality. These models have been the subject of recent work in non-independent component analysis. We show that pairwise mean independence answers the question of how much one can relax independence: it is identifiable, any weaker notion is non-identifiable, and it contains the models previously studied as special cases. Our results apply to distributions with the required zero pattern at any cumulant tensor. We propose an algebraic recovery algorithm based on least-squares optimization over the orthogonal group. Simulations highlight robustness: enforcing full independence can harm estimation, while pairwise mean independence enables more stable recovery. These findings extend the classical ICA framework and provide a rigorous basis for blind source separation beyond independence.