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文献中的一个经典结果表明，对于 $AY = \varepsilon$，若 $\varepsilon$ 的各分量相互独立且至多一个分量为高斯分布，则 $A$ 可被识别至其行向量的符号和排列（Comon, 1994）。本文研究如何通过引入对 $\varepsilon$ 的高阶矩或累积量张量的约束来放松独立性假设。我们给出了若干新条件，证明了若干非独立成分模型（例如公共方差模型）的可识别性，并基于识别结果提出了高效估计方法。研究表明，在无法假设独立性的情形下，相对于依赖独立性的方法，本文方法在效率上可获得显著提升。