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SUMMARY:A concentration interval for the Lasso - Sara Anna van de Geer (ET
 H Zürich)
DTSTART:20180323T090000Z
DTEND:20180323T100000Z
UID:TALK103171@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We consider the linear model and the Lasso estimator. Our goal
  is to provide upper and lower bounds for the prediction error that are cl
 ose to each other. We assume that the active components of the vector of r
 egression coefficients are sufficiently large in absolute value (in a sens
 e that will be specified) and that the tuning parameter is suitably chosen
 .  The bounds depend on so-called compatibility constants. We will present
  the definition of the compatibility constants and discuss their relation 
 with restricted eigenvalues.   As an example\, we consider the  the least 
 squares estimator with total variation penalty  and present bounds with sm
 all 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 th
 at the largest eigenvalue of the covariance matrix remains bounded and est
 ablish under some mild compatibility conditions upper and lower bounds wit
 h ratio tending to one.
LOCATION:Seminar Room 1\, Newton Institute
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