Independent component analysis (ICA) is a fundamental statistical tool used to reveal hidden generative processes from observed data. However, traditional ICA approaches struggle with the rotational invariance inherent in Gaussian distributions, often necessitating the assumption of non-Gaussianity in the underlying sources. This may limit their applicability in broader contexts. To accommodate Gaussian sources, we develop an identifiability theory that relies on second-order statistics without imposing further preconditions on the distribution of sources, by introducing novel assumptions on the connective structure from sources to observed variables. Different from recent work that focuses on potentially restrictive connective structures, our proposed assumption of structural variability is both considerably less restrictive and provably necessary. Furthermore, we propose two estimation methods based on second-order statistics and sparsity constraint. Experimental results are provided to validate our identifiability theory and estimation methods.

翻译：独立成分分析（ICA）是一种用于揭示观测数据背后隐藏生成过程的基本统计工具。然而，传统ICA方法难以处理高斯分布固有的旋转不变性，通常需要假设潜在源具有非高斯性，这可能限制其在更广泛场景中的适用性。为适应高斯源，我们发展了一种基于二阶统计量的可识别性理论，该理论无需对源分布施加进一步的前提条件，而是通过引入关于从源到观测变量的连接结构的新颖假设来实现。与近期关注可能具有限制性的连接结构的研究不同，我们提出的结构变异性假设不仅限制性显著更弱，而且可证明是必要的。此外，我们提出了两种基于二阶统计量与稀疏性约束的估计方法，并提供实验结果以验证我们的可识别性理论与估计方法。