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SUMMARY:Selection and estimation in sparse\, high-dimensional models - Maa
 rten Jansen\, Université libre de Bruxelles
DTSTART:20141010T150000Z
DTEND:20141010T160000Z
UID:TALK54666@talks.cam.ac.uk
CONTACT:20082
DESCRIPTION:In many applications\, the objective of variable selection is 
 to find a good compromise between the likelihood and the complexity of the
  model. The balance between the likelihood and complexity is controlled by
  a regularisation parameter. The selection and estimation thus proceeds in
  two stages. The first step is the assessment of the regularisation parame
 ter\, through the optimisation of an information criterion\, which estimat
 es the distance to the true model.  The second step is then to find the be
 st selection and estimation for a given value of the regularisation parame
 ter.  Obviously\, the former step has to anticipate for effects occurring 
 during the latter step. In particular\, when the class of models under inv
 estigation is high-dimensional while the true model is sparse\, then a rel
 atively large number of false positives may contribute to the likelihood. 
 The impact of false positive selections on the likelihood can be reduced b
 y shrinking the estimates\, especially the smaller ones. This approach\, h
 owever\, makes the selection procedure as a whole too tolerant for false p
 ositives\, leading to a major overestimation of the model size. If we take
  the model size as complexity measure\, then the best estimation within a 
 selection involves no shrinkage. The effect of false positives can then be
  described as a so-called mirror: among the parameters that are not promin
 ently part of the true model\, false positives present themselves as the b
 est candidates for being part of the model\, whereas in reality\, they are
  worse than a random choice of a non-significant parameter.  We present in
 formation criteria that adjust for this mirror effect.
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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