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SUMMARY:Generalized Gauss and Expectation Inequalities via Semidefinite Pr
 ogramming - Paul Goulart\, University of Oxford
DTSTART:20150402T130000Z
DTEND:20150402T140000Z
UID:TALK57916@talks.cam.ac.uk
CONTACT:Tim Hughes
DESCRIPTION:This talk will describe methods for computing sharp upper boun
 ds on the probability of a random vector falling outside of a convex set\,
  or on the expected value of a convex loss function\, for situations in wh
 ich limited information is available about the probability distribution. S
 uch bounds are of interest across many application areas in control theory
 \, mathematical finance\, machine learning and signal processing. If only 
 the first two moments of the distribution are available\, then Chebyshev-l
 ike worst-case bounds can be computed via solution of a single semidefinit
 e program. However\, the results can be very conservative since they are t
 ypically achieved by a discrete worst-case distribution. The talk will sho
 w that considerable improvement is possible if the probability distributio
 n can be assumed unimodal\, in which case less pessimistic Gauss-like boun
 ds can be computed instead. Additionally\, both the Chebyshev- and Gauss-l
 ike bounds for such problems can be derived as special cases of a bound ba
 sed on a generalised definition of unmodality.
LOCATION: Cambridge University Engineering Department\, LR6
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