Montag, 09. November 2020, 16:45 - 17:45 iCal
ISOR Colloquium
! TALK MOVED TO SUMMER SEMESTER 2021 DUE TO COVID19 RESTRICTIONS @UNIVIE !
"Inference in High Dimensions for Generalized Linear Models: the Linear, the Spectral and the Approximate"
Speaker: Marco Mondelli (Institute of Science and Technology Austria)
HS 7 OMP1 (#1.303, 1st floor)
Oskar-Morgenstern-Platz 1, 1090 Wien
Vortrag
In a generalized linear model (GLM), the goal is to estimate a d-dimensional signal x from an n-dimensional observation of the form f(Ax, w), where A is a design matrix and w is a noise vector. Well-known examples of GLMs include phase retrieval, 1-bit compressed sensing, and logistic regression. We focus on the high-dimensional setting in which both the number of measurements n and the signal dimension d diverge, with their ratio tending to a fixed constant.
Linear and spectral methods are two popular solutions to obtain an initial estimate, which can also be used as a ‘warm start’ for other algorithms. In particular, the linear estimator is a data-dependent linear combination of the columns of the design matrix, and its analysis is quite simple; the spectral estimator is the principal eigenvector of a data-dependent matrix, whose spectrum exhibits a phase transition. In this talk, I will first analyze the spectral method and prove that it leads to the information-theoretically optimal threshold for weak recovery in phase retrieval. Second, I will show how to optimally combine the linear and spectral estimators. Finally, I will consider estimators based on approximate message passing (AMP) and prove how to initialize them with the spectral method.
Based on joint work with Andrea Montanari, Christos Thrampoulidis and Ramji Venkataraman
The talk can also be joined online: eu.bbcollab.com/guest/608c5bf7765f4215bb9b46b3646db187
Zur Webseite der Veranstaltung
Veranstalter
Institut für Statistik und Operations Research
Kontakt
Sabine Sobotka-Tompits, BA
Fakultät für Wirtschaftswissenschaften
Institut für Statistik und Operations Research
+43 1 4277 38631
sabine.sobotka-tompits@univie.ac.at
Erstellt am Mittwoch, 04. November 2020, 11:49
Letzte Änderung am Donnerstag, 05. November 2020, 10:15