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CATEGORIES:CCIMI Seminars
SUMMARY:Reconciling Bayesian Regularization And Total Vari
ation Regularization - CCIMI colloquium - Andrew S
tuart\, Caltech
DTSTART;TZID=Europe/London:20180508T170000
DTEND;TZID=Europe/London:20180508T190000
UID:TALK104230AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/104230
DESCRIPTION:The first CCIMI Colloquium will feature a talk by
*Andrew Stuart on 'Reconciling Bayesian Regulariza
tion And Total Variation Regularization'*. This w
ill be held on *Wednesday 8th May at 5pm*\, at the
Centre for Mathematical Sciences\, University of
Cambridge\, and followed with a wine reception.\n\
n*Abstract:*\nJoint work with Matt Dunlop (Caltech
)\, Charlie Elliott (Warwick)\, and Viet Ha Haong
(NTU).\nA central theme in classical algorithms fo
r the reconstruction of discontinuous functions fr
om observational data is perimeter regularization\
, for example via total variation penalization. On
the other hand\, sparse or noisy data often deman
ds a probabilistic approach to the reconstruction
of images\, to enable uncertainty quantification\;
the Bayesian approach to inversion is a natural f
ramework in which to carry this out. The link betw
een Bayesian inversion methods and perimeter regul
arization\, however\, is not fully understood. In
this talk two links are studied: (i) the MAP objec
tive function of a suitably chosen phase-field Bay
esian approach is shown to be closely related to a
least squares plus perimeter regularization objec
tive\; (ii) sample paths of a suitably chosen Baye
sian level set formulation are shown to possess fi
nite perimeter and to have the ability to learn ab
out the true perimeter. Furthermore\, the level se
t approach is shown to lead to faster algorithms f
or uncertainty quantification than the phase field
approach.\n\n*Speaker: Andrew Stuart*\nAndrew Stu
art has research interests in applied and computat
ional mathematics\, and is interested in particula
r in the question of how to optimally combine comp
lex mechanistic models with data. He joined Caltec
h in 2016 as Bren Professor of Computing and Mathe
matical Sciences\, after 17 years as Professor of
Mathematics at the University of Warwick (1999--20
16). Prior to that he was on the faculty in The De
partments of Computer Science and Mechanical Engin
eering at Stanford University (1992--1999)\, and i
n the Mathematics Department at Bath University (1
989--1992). He obtained his PhD from the Oxford Un
iversity Computing Laboratory in 1986\, and held p
ostdoctoral positions in Mathematics at Oxford Uni
versity and at MIT in the period 1986--1989\n\nThe
event is free\, but please register: "https://cci
mi-colloquium-andrew-stuart.eventbrite.co.uk":http
s://ccimi-colloquium-andrew-stuart.eventbrite.co.u
k
LOCATION:MR2 Centre for Mathematical Sciences
CONTACT:Rachel Furner
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