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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:A concentration interval for the Lasso - Sara Anna
van de Geer (ETH Zürich)
DTSTART;TZID=Europe/London:20180323T090000
DTEND;TZID=Europe/London:20180323T100000
UID:TALK103171AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/103171
DESCRIPTION:We consider the linear model and the Lasso estimat
or. Our goal is to provide upper and lower bounds
for the prediction error that are close to each ot
her. We assume that the active components of the v
ector of regression coefficients are sufficiently
large in absolute value (in a sense that will be s
pecified) and that the tuning parameter is suitabl
y chosen. The bounds depend on so-called compatib
ility constants. We will present the definition of
the compatibility constants and discuss their rel
ation with restricted eigenvalues. As an example
\, we consider the the least squares estimator wi
th total variation penalty and present bounds wit
h small gap. For the case of random design\, we
assume that the rows of the design matrix are i.i
.d.copies of a Gaussian random vector. We assume
that the largest eigenvalue of the covariance matr
ix remains bounded and establish under some mild c
ompatibility conditions upper and lower bounds wit
h ratio tending to one.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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