In this paper, we propose a non-parametric score to evaluate the quality of the solution to an iterative algorithm for Independent Component Analysis (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. We also provide a new characteristic function-based contrast function for ICA and propose a fixed point iteration to optimize the corresponding objective function. Finally, we propose a theoretical framework to obtain sufficient conditions for the local and global optima of a family of contrast functions for ICA. This framework uses quasi-orthogonalization inherently, and our results extend the classical analysis of cumulant-based objective functions to noisy ICA. We demonstrate the efficacy of our algorithms via experimental results on simulated datasets.

翻译：本文提出了一种非参数评分方法，用于评估具有任意高斯噪声的独立成分分析（ICA）迭代算法解的质量。该评分的创新之处在于，它仅假设数据具有有限二阶矩，并利用特征函数在不依赖噪声分布参数信息的情况下评估估计混合矩阵的质量。我们还提出了一种基于特征函数的新型ICA对比函数，并采用不动点迭代优化相应目标函数。最后，我们构建了一个理论框架，以获得一类ICA对比函数局部和全局最优解的充分条件。该框架天然地利用了准正交化方法，我们的研究结果将基于累积量的目标函数经典分析拓展到了含噪ICA领域。通过模拟数据集上的实验结果，我们验证了所提算法的有效性。