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SUMMARY:Selection and Clustering of Correlated variables using OWL/GrOWL r
 egularizers - Urvashi Oswal (University of Wisconsin-Madison)
DTSTART:20180627T080000Z
DTEND:20180627T084500Z
UID:TALK107425@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In high-dimensional linear regression problems\, it is likely 
 that several covariates are highly correlated e.g. in fMRI data\, certain 
 voxels or brain regions may have very correlated activation patterns. Usin
 g standard sparsity-inducing regularization (such as Lasso) in such scenar
 ios is known to be unsatisfactory\, as it leads to the selection of a subs
 et of the highly correlated covariates. For engineering purposes and/or sc
 ientific interpretability\, it is often desirable to explicitly identify a
 ll of the covariates that are relevant for modeling the data. In this talk
 \, I will present clustering properties and error bounds of Ordered Weight
 ed $\\ell_1$ (OWL) regularization for linear regression\, and a group vari
 ant for multi-task regression called Group OWL (GrOWL).  I will present th
 e application of OWL/GrOWL in three settings: (1) Brain networks (2) Subsp
 ace clustering and (3) Deep Learning. I will demonstrate\, in theory and e
 xperiments\, how OWL/GrOWL deal with strongly correlated covariates by aut
 omatically clustering and averaging regression coefficients associated wit
 h those covariates.   This is joint work with Robert Nowak\, M&aacute\;rio
  Figueiredo\, Tim Rogers and Chris Cox.
LOCATION:Seminar Room 1\, Newton Institute
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