EE Seminar: Generalized Neyman-Pearson for Multiple Detections
(The talk will be given in English)
Speaker: Dr. Amichai Painsky
HUJI & MIT
Monday, January 7th, 2019
15:00 - 16:00
Room 011, Kitot Bldg., Faculty of Engineering
Generalized Neyman-Pearson for Multiple Detections
Abstract
The classical single hypothesis testing problem considers a set of observations that is drawn from one of two possible distributions, typically denoted as the Null (no signal) and the Alternative (signal). The goal of the test is to maximize the power (correct detection) subject to a prescribed probability of false alarm (false detection). It is well-known that the Neyman-Pearson procedure provides the uniformly most powerful test for the single hypothesis case. However, the problem becomes more complicated when we consider more than two hypotheses. In this work, we formulate the multiple testing problem as an infinite-dimensional optimization problem, seeking the most powerful decision policy under commonly used false detection measures (such as family-wise error rate (FWER) and false discovery rate (FDR)). In this sense, our approach is a generalization of the optimal Neyman-Pearson procedure for testing multiple hypotheses. Using calculus of variations, we show that for exchangeable hypotheses, our problem can be reformulated as infinite linear programs and can be solved for any number of hypotheses, by applying the derived optimality conditions. We demonstrate our results in several setups and show that the power gain over natural competitors is substantial in all the examined settings. Finally, we discuss several engineering applications, from classical communications systems, to more recent sensing devices in autonomous car.
Short Bio
Amichai Painsky is a Post-Doctoral Fellow, co-affiliated with the Israeli Center for Research Excellence in Algorithms (I-CORE ALGO) at the Hebrew University, and the Signals, Information and Algorithms (SIA) Laboratory at MIT. Amichai received his B.Sc. in Electrical Engineering from Tel Aviv University (2007), his M.Eng. in Electrical Engineering from Princeton University (2009) and his Ph.D. in Statistics from Tel Aviv University (2016). He is a recipient an outstanding Ph.D. students award from the school of Mathematical Sciences, the Weinstein Institute of Signal Processing and the Marejn Foundation. Previously, he received a Brain Return Ph.D. Scholarship from the Israeli Center for Returning Scientists.
