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Journal Article

Multiscale blind source separation.

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Munk,  A.
Research Group of Statistical Inverse-Problems in Biophysics, MPI for biophysical chemistry, Max Planck Society;

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Supplementary Material (public)

2586332_Suppl.htm
(Supplementary material), 57KB

Citation

Behr, M., Holmes, C., & Munk, A. (2018). Multiscale blind source separation. The Annals of Statistics, 46(2), 711-744. doi:10.1214/17-AOS1565.


Cite as: http://hdl.handle.net/21.11116/0000-0001-4768-B
Abstract
We provide a new methodology for statistical recovery of single linear mixtures of piecewise constant signals (sources) with unknown mixing weights and change points in a multiscale fashion. We show exact recovery within an epsilon-neighborhood of the mixture when the sources take only values in a known finite alphabet. Based on this we provide the SLAM (Separates Linear Alphabet Mixtures) estimators for the mixing weights and sources. For Gaussian error, we obtain uniform confidence sets and optimal rates (up to log-factors) for all quantities. SLAM is efficiently computed as a nonconvex optimization problem by a dynamic program tailored to the finite alphabet assumption. Its performance is investigated in a simulation study. Finally, it is applied to assign copy-number aberrations from genetic sequencing data to different clones and to estimate their proportions.