Nonparametric Evaluation of Noisy ICA Solutions
This work addresses a domain-specific problem for researchers and practitioners in signal processing and machine learning dealing with noisy ICA, but it is incremental as it builds on existing methods like FASTICA and JADE.
The paper tackles the problem of selecting the best algorithm for Independent Component Analysis (ICA) with arbitrary Gaussian noise by developing a nonparametric score that adaptively picks the right algorithm, and it shows through simulations that this diagnostic can remedy weaknesses in existing methods. It also proposes new contrast functions and algorithms with fast computability and a theoretical framework for convergence analysis.
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.