论文标题
非独立组件分析
Non-Independent Components Analysis
论文作者
论文摘要
ICA文献的开创性结果指出，对于$ ay = \ varepsilon $，如果$ \ varepsilon $的组件是独立的，而最多是高斯，则$ a $被确定以符合其行的符号和固定率（Comon，1994）。在本文中，我们研究了独立假设可以通过在$ \ varepsilon $的高阶或累积张量中限制来替换独立性假设。我们记录了建立多种非独立组件模型的识别的新条件，例如常见方差模型，并根据识别结果提出有效的估计方法。我们表明，在不能假定独立性的情况下，相对于依赖独立性的方法，效率提高可能是重要的。
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.
