Independent Component Analysis (ICA) was introduced in the 1980's as a model for Blind Source Separation (BSS), which refers to the process of recovering the sources underlying a mixture of signals, with little knowledge about the source signals or the mixing process. While there are many sophisticated algorithms for estimation, different methods have different shortcomings. In this paper, we develop a nonparametric score to adaptively pick the right algorithm for ICA with arbitrary Gaussian noise. The novelty of this score stems from the fact that it just assumes a finite second moment of the data and uses the characteristic function to evaluate the quality of the estimated mixing matrix without any knowledge of the parameters of the noise distribution. In addition, we propose some new contrast functions and algorithms that enjoy the same fast computability as existing algorithms like FASTICA and JADE but work in domains where the former may fail. While these also may have weaknesses, our proposed diagnostic, as shown by our simulations, can remedy them. Finally, we propose a theoretical framework to analyze the local and global convergence properties of our algorithms.

翻译：独立成分分析（ICA）于20世纪80年代作为盲源分离（BSS）模型被提出，该模型旨在从信号混合中恢复潜在源信号，且对源信号或混合过程知之甚少。尽管已有多种精密的估计算法，但不同方法各有其局限性。本文提出一种非参数评分，用于自适应选择适用于含任意高斯噪声ICA的合适算法。该评分的创新性在于：仅假设数据具有有限二阶矩，并利用特征函数评估估计混合矩阵的质量，无需任何噪声分布参数信息。此外，我们提出了若干新的对比函数与算法，它们具有与FASTICA和JADE等现有算法同等的快速计算能力，但能在后者可能失效的领域发挥作用。尽管这些方法亦存在缺陷，但模拟实验表明，我们提出的诊断工具可弥补其不足。最后，我们构建了理论框架，分析所提算法的局部与全局收敛特性。