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CATEGORIES:Seminar/Colloquia
DESCRIPTION:SLOPE is a relatively new convex optimization procedure for hig
h-dimensional linear regression via the sorted l1 penalty: the larger the r
ank of the fitted coefficient\, the larger the penalty. This non-separable
penalty renders many existing techniques invalid or inconclusive in analyzi
ng the SLOPE solution. In this talk\, I demonstrate an asymptotically exact
characterization of the SLOPE solution under Gaussian random designs throu
gh solving the SLOPE problem using approximate message passing (AMP). This
characterization of the SLOPE solution allows us to derive the sharp asympt
otic trade-off between the false discovery proportion (FDP) and true positi
ve proportion (TPP) or\, equivalently\, between measures of type I and type
II errors along the SLOPE path. We are able to show that while\, in some p
roblems\, LASSO may have an upper bound of TPP strictly less than 1\, a phe
nomenon known as Donoho-Tanner (DT) phase transition\, our characterization
of the SLOPE trade-off curve shows that SLOPE never suffers from this situ
ation. This is joint work with Zhiqi Bu\, Jason Klusowski\, and Weijie Su
DTEND:20201016T160000Z
DTSTAMP:20201204T114958Z
DTSTART:20201016T150000Z
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SUMMARY:ESE Seminar: Cynthia Rush\, PhD
UID:tag:localist.com\,2008:EventInstance_34740355858578
URL:https://happenings.wustl.edu/event/ese_seminar_cynthia_rush_phd
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