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CATEGORIES:CUED Control Group Seminars
SUMMARY:Generalized Gauss and Expectation Inequalities via
Semidefinite Programming - Paul Goulart\, Univers
ity of Oxford
DTSTART;TZID=Europe/London:20150402T140000
DTEND;TZID=Europe/London:20150402T150000
UID:TALK57916AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/57916
DESCRIPTION:This talk will describe methods for computing shar
p upper bounds on the probability of a random vect
or falling outside of a convex set\, or on the exp
ected value of a convex loss function\, for situat
ions in which limited information is available abo
ut the probability distribution. Such bounds are o
f interest across many application areas in contro
l theory\, mathematical finance\, machine learning
and signal processing. If only the first two mome
nts of the distribution are available\, then Cheby
shev-like worst-case bounds can be computed via so
lution of a single semidefinite program. However\,
the results can be very conservative since they a
re typically achieved by a discrete worst-case dis
tribution. The talk will show that considerable im
provement is possible if the probability distribut
ion can be assumed unimodal\, in which case less p
essimistic Gauss-like bounds can be computed inste
ad. Additionally\, both the Chebyshev- and Gauss-l
ike bounds for such problems can be derived as spe
cial cases of a bound based on a generalised defin
ition of unmodality.
LOCATION: Cambridge University Engineering Department\, LR6
CONTACT:Tim Hughes
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