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SUMMARY:On the Sample Complexity of Learning with Geometric Stability - Al
 berto Bietti (NYU)
DTSTART:20220209T140000Z
DTEND:20220209T150000Z
UID:TALK169127@talks.cam.ac.uk
CONTACT:Willem Diepeveen
DESCRIPTION:Many supervised learning problems involve high-dimensional dat
 a such as images\, text\, or graphs. In order to make efficient use of dat
 a\, it is often useful to leverage certain geometric priors in the problem
  at\nhand\, such as invariance to translations\, permutation subgroups\, o
 r stability to small deformations. We study the sample complexity of learn
 ing problems where the target function presents such invariance and stabil
 ity properties\, by considering spherical harmonic decompositions of such 
 functions on the sphere. We provide non-parametric rates of convergence fo
 r kernel methods\, and show improvements in sample complexity by a factor 
 equal to the size of the group when using an invariant kernel over the gro
 up\, compared to the\ncorresponding non-invariant kernel. These improvemen
 ts are valid when the sample size is large enough\, with an asymptotic beh
 avior that depends on spectral properties of the group. Finally\, these ga
 ins are\nextended beyond invariance groups to also cover geometric stabili
 ty to small deformations\, modeled here as subsets (not necessarily subgro
 ups) of permutations.\n\n\n*Join Zoom Meeting*\nhttps://maths-cam-ac-uk.zo
 om.us/j/98587671557?pwd=eGthTEU5TVdNcUt0bldQREhMaVhMZz09\n\nMeeting ID: 98
 5 8767 1557\nPasscode: 169824\n
LOCATION:Virtual (Zoom details under abstract)
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