Exact Asymptotics with Approximate Message Passing and a Study of the Type 1-Type 2 Error Trade-off for SLOPE
Abstract
Approximate message passing is a class of iterative algorithms that can be used to systematically derive exact expressions for the asymptotic risk and other performance metrics for estimators that are constructed as solutions to a broad class of convex optimization problems. In this talk, the speaker will present a general program for using AMP in this way and provide a specific example by using this approach to study the asymptotic model selection properties of sorted L1 penalized estimation (SLOPE). Sorted L1 regularization has been incorporated into many methods for solving high-dimensional statistical estimation problems, including using SLOPE in the context of linear regression. The speaker will show how this regularization technique improves variable selection relative to the LASSO by characterizing the optimal SLOPE trade-off between the false discovery proportion and true positive proportion or, equivalently, between measures of type I and type II error. Collaborators on this work include Zhiqi BU, Jason KLUSOWSKI, and Weijie SU (https://arxiv.org/abs/1907.07502 and https://arxiv.org/abs/2105.13302) and Oliver FENG, Ramji VENKATARAMANAN, and Richard SAMWORTH (https://arxiv.org/abs/2105.02180).
About the Speaker
Prof. Cynthia RUSH received a PhD and MA in Statistics from Yale University in 2016 and 2011, respectively, and she completed her undergraduate coursework at the University of North Carolina at Chapel Hill where she obtained a BS in Mathematics in 2010. She joined Columbia University in 2016 and is currently the Howard Levene Assistant Professor in the Department of Statistics. She is also the Affiliated Member of the Data Science Institute at Columbia University.
Prof. Rush’s research uses tools and ideas from information theory, statistical physics, and applied probability as a framework for understanding modern, high-dimensional inference and estimation problems and complex machine learning tasks that are core challenges in the fields of statistics and data science.
Prof. Rush is the recipient of the 2019 Computer and Information Science and Engineering Research Initiation Initiative grant from the US National Science Foundation. She was also an NTT Research Fellow at the Simons Institute for the Theory of Computing for the program on Probability, Computation, and Geometry in High Dimensions in Fall 2020 and a Google Research Fellow at the Simons Institute for the Theory of Computing for the program on Computational Complexity of Statistical Inference in Fall 2021.
For Attendees' Attention
Seating is on a first come, first served basis.
