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 the cumulants of $\varepsilon$. We document minimal cumulant conditions for identifiability and propose efficient estimation methods based on the new identification results. In situations where independence cannot be assumed the efficiency gains can be significant relative to methods that rely on independence. The proof strategy employed highlights new geometric and combinatorial tools that can be adopted to study identifiability via higher order restrictions in linear systems.

翻译：ICA文献的一项重大成果指出,对于$AY = varepsilon$,如果美元的组成部分是独立的,最多一个是Gaussian,那么就确定$A$,以签署和调整其行[Comon, 1994]。在本文件中,我们研究独立假设在多大程度上可以通过限制积聚$varepsilon美元而予以放松。我们记录了可识别性的最低累积条件,并根据新的识别结果提出了有效的估算方法。在无法假定独立效率收益与依赖独立的方法相比可能具有重大意义的情况下,采用的证据战略突出新的几何和组合工具,这些工具可以通过线性系统更高的定序限制来研究可识别性。