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SUMMARY:Hilbert Space Embedding of Probability Measures: Theory and Applic
 ations - Bharath Sriperumbudur
DTSTART:20120309T160000Z
DTEND:20120309T170000Z
UID:TALK36805@talks.cam.ac.uk
CONTACT:Richard Samworth
DESCRIPTION:Modern scientific fields (e.g.\, social sciences\, bioinformat
 ics\, biomedical\nimaging and genomics) routinely deal with high-dimension
 al and highly\ncomplex information\, including data from non-Euclidean spa
 ces such as trees\,\ngraphs and strings. In this talk\, I will introduce a
  functional analytic\nmethod for representing and analyzing high-dimension
 al and complex data by\nembedding probability measures into a reproducing 
 kernel Hilbert space\n(RKHS). Such embeddings can be seen as a generalizat
 ion of characteristic\nfunction associated with a probability measure. Thi
 s generalization allows\nus to represent and compare random variables on d
 omains more general than\nR^n (including graphs\, strings\, and groups)\, 
 which can then be exploited in\nmany statistical applications like homogen
 eity/independence/goodness-of-fit\ntesting\, feature selection and density
  estimation. I will discuss various\ntheoretical questions related to dist
 ribution embeddings\, for example\, when\nis the embedding injective and h
 ow it is related to the properties of the\nRKHS? I will then present two a
 pplications of the embedding in two-sample\ntesting and mixture sieve dens
 ity estimation. Finally\, I will conclude by\ndiscussing some open problem
 s and ongoing/future research directions.\n\nJoint work with Kenji Fukumiz
 u (The Institute of Statistical Mathematics)\,\nArthur Gretton (Gatsby Com
 putational Neuroscience Unit\, UCL)\, Gert Lanckriet\n(UC San Diego) and B
 ernhard Scholkopf (Max Planck Institute for Intelligent\nSystems)\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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