Joint low-rank approximation for extracting non-Gaussian subspaces
Signal Processing
A Linear Non-Gaussian Acyclic Model for Causal Discovery
The Journal of Machine Learning Research
Image Source Separation Using Color Channel Dependencies
ICA '09 Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation
The Journal of Machine Learning Research
A novel dimension reduction procedure for searching non-gaussian subspaces
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Testing significance of mixing and demixing coefficients in ICA
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
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A blind separation problem where the sources are not independent, but have variance dependencies is discussed. For this scenario Hyvärinen and Hurri (2004) proposed an algorithm which requires no assumption on distributions of sources and no parametric model of dependencies between components. In this paper, we extend the semiparametric approach of Amari and Cardoso (1997) to variance dependencies and study estimating functions for blind separation of such dependent sources. In particular, we show that many ICA algorithms are applicable to the variance-dependent model as well under mild conditions, although they should in principle not. Our results indicate that separation can be done based only on normalized sources which are adjusted to have stationary variances and is not affected by the dependent activity levels. We also study the asymptotic distribution of the quasi maximum likelihood method and the stability of the natural gradient learning in detail. Simulation results of artificial and realistic examples match well with our theoretical findings.