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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:A statistical perspective on sparse regularization
and geometric modelling - Aykroyd\, R (University
of Leeds)
DTSTART;TZID=Europe/London:20140207T134500
DTEND;TZID=Europe/London:20140207T143000
UID:TALK50710AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/50710
DESCRIPTION:Consider a typical inverse problem where we wish t
o reconstruct an unknown function from a set of me
asurements. When the function is discretized it is
usual for the number of data points to be insuffi
cient to uniquely determine the unknowns the prob
lem is ill-posed. One approach is to reduce the si
ze of the set of eligible solutions until it conta
ins only a single solutionthe problem is regulariz
ed. There are\, however\, infinitely many possible
restrictions each leading to a unique solution. H
ence the choice of regularization is crucial\, but
the best choice\, even amongst those commonly use
d\, is still difficult. Such regularized reconstru
ction can be placed into a statistical setting whe
re data fidelity becomes a likelihood function and
regularization becomes a prior distribution. Reco
nstruction then becomes a statistical inference ta
sk solved\, perhaps\, using the posterior mode. Th
e common regularization approaches then correspond
to different choices of prior di stribution. In t
his talk the ideas of regularized estimation\, inc
luding ridge\, lasso\, bridge and elastic-net regr
ession methods\, will be defined. Application of s
parse regularization to basis function expansions\
, and other dictionary methods\, such as wavelets
will be discussed. Their link to smooth and sparse
regularization\, and to Bayesian estimation\, wil
l be considered. As an alternative to locally cons
trained reconstruction methods\, geometric models
impose a global structure. Such models are usually
problem specific\, compared to more generic local
ly constrained methods\, but when the parametric a
ssumptions are reasonable they will make better us
e of the data\, provide simpler models and can inc
lude parameters which may be used directly\, for e
xample in monitoring or control\, without the need
for extra post-processing. Finally\, the matching
of modelling and estimation styles with numerical
procedures\, to produce efficient algorithms\, wi
ll be discussed.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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