Multiscale Blind Source Separation

Behr M, Holmes C, Munk A (2018)

Publication Type: Journal article

Publication year: 2018

Journal

Annals of Statistics Institute of Mathematical Statistics (IMS)

Book Volume: 46

Pages Range: 711-744

Journal Issue: 2

DOI: 10.1214/17-AOS1565

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.

Involved external institutions

Georg-August-Universität Göttingen DE Germany (DE) University of Oxford GB United Kingdom (GB)

How to cite

APA:

Behr, M., Holmes, C., & Munk, A. (2018). Multiscale Blind Source Separation. Annals of Statistics, 46(2), 711-744. https://dx.doi.org/10.1214/17-AOS1565

MLA:

Behr, Merle, Chris Holmes, and Axel Munk. "Multiscale Blind Source Separation." Annals of Statistics 46.2 (2018): 711-744.

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