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SUMMARY:Optimal kernel choice for kernel hypothesis testing - Arthur Grett
 on\, UCL
DTSTART:20121116T140000Z
DTEND:20121116T150000Z
UID:TALK41463@talks.cam.ac.uk
CONTACT:Microsoft Research Cambridge Talks Admins
DESCRIPTION:We consider two nonparametric hypothesis testing problems: (1)
  Given samples from distributions p and q\, a two-sample test determines w
 hether to reject the null hypothesis p=q\; and (2) Given a joint distribut
 ion p_xy over random variables x and y\, an independence test determines w
 hether to reject the null hypothesis of independence\, p_xy = p_x p_y. In 
 testing whether two distributions are identical\, or whether two random va
 riables are independent\, we require a test statistic which is a measure o
 f distance between probability distributions. One choice of test statistic
  is the maximum mean discrepancy (MMD)\, a distance between embeddings of 
 the probability distributions in a reproducing kernel Hilbert space. The k
 ernel used in obtaining these embeddings is critical in ensuring the test 
 has high power\, and correctly distinguishes unlike distributions with hig
 h probability.\n\nIn this talk\, I will provide a tutorial overview of ker
 nel distances on probabilities\, and show how these may be used in two-sam
 ple and independence testing. I will then describe a strategy for optimal 
 kernel choice\, and compare it with earlier heuristics (including other mu
 ltiple kernel learning approaches).\n\nJoint work with: Bharath Sriperumbu
 dur\, Dino Sejdinovic\, Heiko Strathmann\, Sivaraman Balakrishnan\, Massim
 iliano Pontil\, Kenji Fukumizu
LOCATION:Large lecture theatre\, Microsoft Research Ltd\, 7 J J Thomson Av
 enue (Off Madingley Road)\, Cambridge
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