Hypothesis Testing in Independent Component Analysis / Blind Source Separation

Independent component analysis (ICA) is a widely used technique for extracting latent (unobserved) source signals from observed multidimensional measurements. Up to date, the estimation problems in ICA are thoroughly studied whereas the statistical inference (hypothesis testing) in ICA is still in its infancy. In this thesis we construct fast and robust bootstrap hypotheses on the coefficients of the mixing matrix in ICA model to investigate contribution of a specific source signal-of-interest onto a specific sensor (mixture variable). Such testing procedure can be used e.g. to detect if a mixture is severely affected by a specific kind of noise or to propose an optimum setup of the recording sensors, which facilitates dimensionality reduction in high-dimensional signal separation problems. The fast and robust bootstrap method has given the tests great potential of being used in real-world ICA analysis of high-dimensional data sets e.g. in biomedical applications