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SUMMARY:An overview of covariance operators in Hilbert space\, and their a
 pplications - Arthur Gretton
DTSTART:20071107T140000Z
DTEND:20071107T150000Z
UID:TALK9070@talks.cam.ac.uk
CONTACT:Karsten Borgwardt
DESCRIPTION:Many problems in unsupervised learning require the analysis\no
 f features of probability distributions. In this talk\, we deal with\nthe 
 problem of measuring dependence between random variables\, using\nthe cova
 riance between maps of these variables to spaces of\nfeatures. When the fe
 ature spaces are universal reproducing kernel\nHilbert spaces (RKHSs)\, it
  can be shown that the covariance is zero\nonly when the variables are ind
 ependent.\n\nA different perspective on these operators arises when one se
 eks to\nmanipulate variables so as to maximise their dependence (as measur
 ed\nby feature space covariance)\, rather than minimising it. In the case\
 nof feature selection\, we would choose those features that maximise the\n
 dependence with respect to particular target variables. Several\nwell-know
 n feature selection algorithms can be recovered through an\nappropriate fe
 ature space choice. Finally\, covariance operators may\nbe combined to giv
 e measures of conditional covariance\, which may be\nused to measure condi
 tional dependence.
LOCATION:Engineering Department\, CBL Room 438
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