独立分量分析中可辨识性的量化
Quantifying identifiability in independent component analysis
摘要：
当误差分布接近高斯分布（但不同于高斯分布）时，我们对ICA模型中混合矩阵的一致估计感兴趣。特别地，我们考虑来自ICA模型$X = Aε$的$n$独立样本，其中我们假设$ε$的坐标根据受污染的高斯分布独立且同分布，并且允许污染量取决于$n$。然后，我们研究如何一致地估计混合矩阵的能力取决于污染的量。我们的研究结果表明，在渐近意义上，如果污染量以$1/\sqrt{n}$或更快的速度减少，那么混合矩阵只能识别转置产品。这些结果也有影响的因果关系推断，从线性结构方程模型与近高斯加性噪声。
英文摘要：
We are interested in consistent estimation of the mixing matrix in the ICA model, when the error distribution is close to (but different from) Gaussian. In particular, we consider $n$ independent samples from the ICA model $X = Aε$, where we assume that the coordinates of $ε$ are independent and identically distributed according to a contaminated Gaussian distribution, and the amount of contamination is allowed to depend on $n$. We then investigate how the ability to consistently estimate the mixing matrix depends on the amount of contamination. Our results suggest that in an asymptotic sense, if the amount of contamination decreases at rate $1/\sqrt{n}$ or faster, then the mixing matrix is only identifiable up to transpose products. These results also have implications for causal inference from linear structural equation models with near-Gaussian additive noise.
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