Statistical Analysis of Sample-Size Effects in ICA

摘要

Independent component analysis (ICA) solves the blind source separation problem by evaluating higher-order statistics, e.g. by estimating fourth-order moments. While estimation errors of the kurtosis can be shown to asymptotically decay with sample size according to a square-root law, they are subject to two further effects for finite samples. Firstly, errors in the estimation of kurtosis increase with the deviation from Gaussianity. Secondly, errors in kurtosis-based ICA algorithms increase when approaching the Gaussian case. These considerations allow us to derive a strict lower bound for the sample size to achieve a given separation quality, which we study analytically for a specific family of distributions and a particular algorithm (fastICA). We further provide results from simulations that support the relevance of the analytical results.