  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.
