提出更宽松的可识别性条件，突破传统独立成分分析局限。
Beyond independent component analysis: identifiability and algorithms
- 用成对均值独立替代完全独立，实现更强的可识别性。
- 在仿真中证明：强制独立反而降低估计稳定性。
- 适合需要鲁棒盲源分离的研究者参考。
独立成分分析（ICA）是恢复潜在变量的经典方法，具有良好的可识别性。当变量独立时，累积量张量呈对角结构；放宽独立性假设后，累积量张量的零结构推广了对角性。近年来，非独立成分分析模型受到关注。本文表明，成对均值独立是可放松独立性的最优条件：它具备可识别性，任何更弱的条件均不可识别，且包含此前研究的模型作为特例。该结论适用于任意具有所需零模式的累积量张量分布。我们提出一种基于正交群上最小二乘优化的代数恢复算法。仿真结果表明，强制完全独立会损害估计性能，而采用成对均值独立能实现更稳定的恢复。这些发现扩展了经典ICA框架，为超越独立性的盲源分离提供了严格理论基础。
原文摘要 · Abstract (English)
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.
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