Abstract. We first review some rigorous properties of the Hermite polynomials, and demonstrate their usefulness in estimating probability distributions as series from data samples. We then proceed to explain how these series can be used to obtain precise and robust measures of nonGaussianity. Our measures of non-Gaussianity detect all kinds of deviations from Gaussianity, and thus provide reliable objective functions for ICA. With a linear computational complexity with respect to the sample size, our method is also suitable for large data sets.
We present new results about the simultaneous linear inverse problems using independent component analysis (ICA), which can be used to separate the data into statistically independent components. The idea of using ICA in solving such inverse problems, especially in EEG/MEG context, has been a known topic for at least more than a decade, but the known results have been justified heuristically, and their relationships are not understood properly. Here we show how to obtain a Bayesian posterior for a spatial source distribution, by using an ICA demixing matrix as an input. The posterior enables us to rederive and reinterpret the previously known methods, and also provides completely new methods.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.