Seminar in applied mathematics and statistics – University of Copenhagen

Seminar in applied mathematics and statistics

SPEAKER: Axel Munk (Georg August Universität Göttingen)

TITLE: Multiscale Blind Source Separation

ABSTRACT: We discuss a new methodology for statistical recovery of single linear mixtures of piecewise constant signals (sources) with unknown mixing weights in a multiscale fashion. This problems occurs in a variety of areas, ranging from telecommunications  and electrophysiology to cancer genetics. We show that exact recovery within a small neighborhood of the mixture is possible when the sources take values in a known finite set. In a sense this can be understood as a certain kind of sparsity. Based on this we provide the SLAM (Separates Linear Alphabet Mixtures) estimators and confidence statements for the mixing weights and sources. For Gaussian error we present some theory, e.g. 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 (CNAs) from genetic sequencing data to different tumor clones and to estimate their proportions.

This is joint work with Merle Behr (Göttingen) and Chris Holmes (Oxford).

Tea and chocolate will be served in room 04.4.19 after the seminar.


Upcoming seminars:

February 9, 13:15: Peter Harremoës (Copenhagen Business College)

April 6, 13:15: Kayvan Sadeghi (Cambridge)