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  Multiscale blind source separation.

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

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Item Permalink: http://hdl.handle.net/21.11116/0000-0001-4768-B Version Permalink: http://hdl.handle.net/21.11116/0000-0003-31B3-B
Genre: Journal Article

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 Creators:
Behr, M., Author
Holmes, C., Author
Munk, A.1, Author              
Affiliations:
1Research Group of Statistical Inverse-Problems in Biophysics, MPI for biophysical chemistry, Max Planck Society, ou_1113580              

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Free keywords: Multiscale inference; honest confidence sets; change point regression; finite alphabet linear mixture; exact recovery; genetic sequencing
 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.

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Language(s): eng - English
 Dates: 2018-04-032018-04
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: Peer
 Identifiers: DOI: 10.1214/17-AOS1565
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Title: The Annals of Statistics
Source Genre: Journal
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Pages: - Volume / Issue: 46 (2) Sequence Number: - Start / End Page: 711 - 744 Identifier: -