October 2021
Revealing the simplicity of high-dimensional objects via pathwise analysis
Ronen Eldan (Weizmann Inst. of Science and Princeton)
Abstract: One of the main reasons behind the success of high-dimensional statistics and modern machine learning in taming the curse of dimensionality is that many classes of high-dimensional distributions are surprisingly well-behaved and, when viewed correctly, exhibit a simple structure. This emergent simplicity is in the center of the theory of "high-dimensional phenomena", and is manifested in principles such as "Gaussian-like behavior" (objects of interest often inherit the properties of the Gaussian measure), "dimension-free behavior" (expressed in inequalities which do…
Find out more »November 2021
Characterizing the Type 1-Type 2 Error Trade-off for SLOPE
Cynthia Rush (Columbia University)
Abstract: Sorted L1 regularization has been incorporated into many methods for solving high-dimensional statistical estimation problems, including the SLOPE estimator in linear regression. In this talk, we study how this relatively new regularization technique improves variable selection by characterizing the optimal SLOPE trade-off between the false discovery proportion (FDP) and true positive proportion (TPP) or, equivalently, between measures of type I and type II error. Additionally, we show that on any problem instance, SLOPE with a certain regularization sequence outperforms…
Find out more »December 2021
