Special Statistics Lecture
STA 290 Seminar Series
Friday, October 7th, 11:10am, MSB 1147 (Colloquium Room)
Refreshments at 12:30 in MSB 1147 following the seminar.
Speaker: Axel Munk (Georg August Universität Göttingen, Germany)
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 and change points 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 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 (CNAs) from genetic sequencing data to different tumor clones and to estimate their proportions. The first half of the talk is non technical and I aim to give an intuition on this problem by many examples. This is joint work with Merle Behr (Göttingen) and Chris Holmes (Oxford).