Abstract

In high-dimensional linear regression (and other inverse problems), highly correlated variables/covariates are a challenge to variable selection procedures. In those scenarios, standard sparsity-inducing regularization (namely l1, a.k.a. LASSO ) is inadequate, as it leads to the selection of arbitrary convex combinations of those variables, maybe even of an arbitrary subset thereof. However, specially in scientific contexts, it is often important to explicitly identify all the relevant covariates, as well as explicitly identify groups/clusters thereof. This talk addresses the recently introduced ordered weighted l1 regularizer, which has been proposed for this purpose. We review several convex optimization aspects concerning this regularizer, show sufficient conditions for exact clustering, and characterize its statistical performance.

Bio: Mário A. T. Figueiredo received a PhD in electrical and computer engineering, from Instituto Superior Técnico (IST), the engineering school of the University of Lisbon, in 1994. He has been with the faculty of the Department of Electrical and Computer Engineering, IST , since 1994, where he is now a Professor. He is also area coordinator and group leader at Instituto de Telecomunicações, a private non-profit research institute. His research interests include image processing and analysis, machine learning, and optimization. M. Figueiredo is a Fellow of the IEEE and of the IAPR and is included in the 2014 and 2015 Thomson Reuters’ Highly Cited Researchers lists; he received several awards, namely the 2011 IEEE Signal Processing Society Best Paper Award, the 2014 IEEE W . R. G. Baker Award, and the 2016 EURASIP Individual Technical Achievement Award.