A seminal result in the ICA literature states that for $AY = \varepsilon$, if the components of $\varepsilon$ are independent and at most one is Gaussian, then $A$ is identified up to sign and permutation of its rows (Comon, 1994). In this paper we study to which extent the independence assumption can be relaxed by replacing it with restrictions on higher order moment or cumulant tensors of $\varepsilon$. We document new conditions that establish identification for several non-independent component models, e.g. common variance models, and propose efficient estimation methods based on the identification results. We show that in situations where independence cannot be assumed the efficiency gains can be significant relative to methods that rely on independence.

翻译：ICA文献中的一个开创性成果表明，对于 $AY = \varepsilon$，若 $\varepsilon$ 的各分量独立且至多一个为高斯分布，则 $A$ 可被识别至行向量的符号和排列（Comon, 1994）。本文研究独立性假设可在何种程度上被放宽，即通过将独立性替换为对 $\varepsilon$ 的高阶矩或累积量张量的约束条件。我们提出了若干新条件，这些条件为多种非独立成分模型（例如共同方差模型）建立了识别性，并基于识别结果提出了高效估计方法。我们证明，在无法假设独立性的情形下，相较于依赖独立性的方法，本文方法的效率提升可能十分显著。