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SUMMARY:Adaptive two-sample testing - Arthur Gretton (Gatsby Computational
  Neuroscience Unit\, UCL)
DTSTART:20231027T130000Z
DTEND:20231027T140000Z
UID:TALK206011@talks.cam.ac.uk
CONTACT:Qingyuan Zhao
DESCRIPTION:I will address the problem of  two-sample testing using the Ma
 ximum Mean Discrepancy (MMD). The MMD is an integral probability metric de
 fined using a reproducing kernel Hilbert space (RKHS)\, with properties de
 termined by the choice of kernel. For good test power\, the kernel must be
  chosen in accordance with the properties of the distributions being compa
 red. \nI will address two cases:\n*  The distributions being tested have d
 ensities\, and the difference in densities lies in a Sobolev ball. The MMD
  test is then minimax optimal with a specific kernel depending on the smoo
 thness parameter of the Sobolev ball. In practice\, this parameter is unkn
 own: to overcome this issue\, I describe an aggregated test\, called MMDAg
 g\, which is adaptive to the smoothness parameter. The test power is maxim
 ised over the collection of kernels used\, without requiring held-out data
  for kernel selection (which results in a loss of test power). MMDAgg cont
 rols the test level non-asymptotically\, and achieves the minimax rate ove
 r Sobolev balls\, up to an iterated logarithmic term. Guarantees hold for 
 any product of one-dimensional translation invariant characteristic kernel
 s.\n* The distributions being tested may not have densities\, but might be
  high dimensional (eg distributions over images)\, In this case\, I will d
 escribe a heuristic for training neural net features for two-sample testin
 g\, by maximizing a proxy for test power over a held-out data set. This yi
 elds state-of-the-art performance on challenging real-world problems\, for
  instance distinguishing between distributions over CIFAR images.
LOCATION:MR12\, Centre for Mathematical Sciences
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