Multiscale Blind Source Separation
2018 | journal article. A publication with affiliation to the University of Göttingen.
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Details
- Authors
- Behr, Merle ; Holmes, Chris; Munk, Axel
- 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 ϵ-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.
- Issue Date
- 2018
- Journal
- The Annals of Statistics
- Project
- RTG 2088: Research Training Group 2088 Discovering structure in complex data: Statistics meets Optimization and Inverse Problems
- Organization
- Max-Planck-Institut für Biophysikalische Chemie
- ISSN
- 0090-5364
- Language
- English