Blind source separation (BSS) aims to recover an unobserved signal $S$ from its mixture $X=f(S)$ under the condition that the effecting transformation $f$ is invertible but unknown. As this is a basic problem with many practical applications, a fundamental issue is to understand how the solutions to this problem behave when their supporting statistical prior assumptions are violated. In the classical context of linear mixtures, we present a general framework for analysing such violations and quantifying their impact on the blind recovery of $S$ from $X$. Modelling $S$ as a multidimensional stochastic process, we introduce an informative topology on the space of possible causes underlying a mixture $X$, and show that the behaviour of a generic BSS-solution in response to general deviations from its defining structural assumptions can be profitably analysed in the form of explicit continuity guarantees with respect to this topology. This allows for a flexible and convenient quantification of general model uncertainty scenarios and amounts to the first comprehensive robustness framework for BSS. Our approach is entirely constructive, and we demonstrate its utility with novel theoretical guarantees for a number of statistical applications.

翻译：盲源分离（BSS）旨在从混合信号 $X=f(S)$ 中恢复未知信号 $S$，其前提是变换函数 $f$ 可逆但未知。由于这是一个具有众多实际应用的基本问题，理解该问题解在其支撑的统计先验假设被违反时的行为特性，便成为一项基础性议题。针对经典线性混合场景，我们提出一个通用框架，用于分析此类假设违反情形并量化其对从 $X$ 中盲恢复 $S$ 的影响。通过将 $S$ 建模为多维随机过程，我们在可能构成混合信号 $X$ 的成因空间上引入一种信息拓扑结构，并证明：通用BSS解对于其定义性结构假设的一般性偏离所产生的响应，可借助关于该拓扑的显式连续性保证进行有效分析。这为一般模型不确定性场景提供了一种灵活便捷的量化方法，并构成了首个针对BSS的综合性鲁棒性分析框架。我们的方法完全具有构造性，并通过若干统计应用中的新颖理论保证验证了其实用性。