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CATEGORIES:Statistics
SUMMARY:Selection and estimation in sparse\, high-dimensio
nal models - Maarten Jansen\, Université libre de
Bruxelles
DTSTART;TZID=Europe/London:20141010T160000
DTEND;TZID=Europe/London:20141010T170000
UID:TALK54666AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/54666
DESCRIPTION:In many applications\, the objective of variable s
election is to find a good compromise between the
likelihood and the complexity of the model. The ba
lance between the likelihood and complexity is con
trolled by a regularisation parameter. The selecti
on and estimation thus proceeds in two stages. The
first step is the assessment of the regularisatio
n parameter\, through the optimisation of an infor
mation criterion\, which estimates the distance to
the true model. The second step is then to find
the best selection and estimation for a given valu
e of the regularisation parameter. Obviously\, th
e former step has to anticipate for effects occurr
ing during the latter step. In particular\, when t
he class of models under investigation is high-dim
ensional while the true model is sparse\, then a r
elatively large number of false positives may cont
ribute to the likelihood. The impact of false posi
tive selections on the likelihood can be reduced b
y shrinking the estimates\, especially the smaller
ones. This approach\, however\, makes the selecti
on procedure as a whole too tolerant for false pos
itives\, leading to a major overestimation of the
model size. If we take the model size as complexit
y measure\, then the best estimation within a sele
ction involves no shrinkage. The effect of false p
ositives can then be described as a so-called mirr
or: among the parameters that are not prominently
part of the true model\, false positives present t
hemselves as the best candidates for being part of
the model\, whereas in reality\, they are worse t
han a random choice of a non-significant parameter
. We present information criteria that adjust for
this mirror effect.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:
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