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SUMMARY:Sharp bounds for compressive learning - Ata Kaban\, University of 
 Birmingham
DTSTART:20140117T160000Z
DTEND:20140117T170000Z
UID:TALK49562@talks.cam.ac.uk
CONTACT:20082
DESCRIPTION:The first part of the talk will derive sharp bounds on the gen
 eralization error of a generic linear classifier trained by empirical risk
  minimization on randomly-projected data. We make no restrictive assumptio
 ns on the data -- such as sparsity\, separability\, or distributional assu
 mptions. Instead\, by using elementary\ntechniques\, we derive the exact p
 robability of label flipping under Gaussian random projection and use this
  to bound the effect of random projection on the generalisation error of t
 he compressive classifier.\nThe second part of the talk will present an an
 alogous strategy for regression. This provides a new analysis of the exces
 s risk of compressive linear least squares\, which removes a spurious log(
 N) factor from previous bounds (where N is the number of training points).
  In addition to tightness\, these new bounds have a clear interpretation a
 nd reveal meaningful structural properties of the learning problem that ma
 ke them solvable effectively in a small dimensional random subspace.\n
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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