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CATEGORIES:CCIMI Seminars
SUMMARY:On the Sample Complexity of Learning with Geometri
c Stability - Alberto Bietti (NYU)
DTSTART;TZID=Europe/London:20220209T140000
DTEND;TZID=Europe/London:20220209T150000
UID:TALK169127AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/169127
DESCRIPTION:Many supervised learning problems involve high-dim
ensional data such as images\, text\, or graphs. I
n order to make efficient use of data\, it is ofte
n useful to leverage certain geometric priors in t
he problem at\nhand\, such as invariance to transl
ations\, permutation subgroups\, or stability to s
mall deformations. We study the sample complexity
of learning problems where the target function pre
sents such invariance and stability properties\, b
y considering spherical harmonic decompositions of
such functions on the sphere. We provide non-para
metric rates of convergence for kernel methods\, a
nd show improvements in sample complexity by a fac
tor equal to the size of the group when using an i
nvariant kernel over the group\, compared to the\n
corresponding non-invariant kernel. These improvem
ents are valid when the sample size is large enoug
h\, with an asymptotic behavior that depends on sp
ectral properties of the group. Finally\, these ga
ins are\nextended beyond invariance groups to also
cover geometric stability to small deformations\,
modeled here as subsets (not necessarily subgroup
s) of permutations.\n\n\n*Join Zoom Meeting*\nhttp
s://maths-cam-ac-uk.zoom.us/j/98587671557?pwd=eGth
TEU5TVdNcUt0bldQREhMaVhMZz09\n\nMeeting ID: 985 87
67 1557\nPasscode: 169824\n
LOCATION:Virtual (Zoom details under abstract)
CONTACT:Willem Diepeveen
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