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SUMMARY:Kernel Quantile Embeddings and Associated Probability Metrics - Ma
 sha Naslidnyk (University College London)
DTSTART:20250506T143000Z
DTEND:20250506T153000Z
UID:TALK230452@talks.cam.ac.uk
DESCRIPTION:Embedding probability distributions into reproducing kernel Hi
 lbert spaces (RKHS) has enabled powerful non-parametric methods such as th
 e maximum mean discrepancy (MMD)\, a statistical distance with strong theo
 retical and computational properties. At its core\, the MMD relies on kern
 el mean embeddings (KMEs) to represent distributions as mean functions in 
 RKHS. However\, it remains unclear if the mean function is the only meanin
 gful RKHS representation.Inspired by generalised quantiles\, we introduce 
 the notion of kernel quantile embeddings (KQEs)\, along with a consistent 
 estimator. We then use KQEs to construct a family of distances that:(i) ar
 e probability metrics under weaker kernel conditions than MMD\;(ii) recove
 r a kernelised form of the sliced Wasserstein distance\; and(iii) can be e
 fficiently estimated with near-linear cost.Through hypothesis testing\, we
  show that these distances offer a competitive alternative to MMD and its 
 fast approximations. Our findings demonstrate the value of representing di
 stributions in Hilbert space beyond simple mean functions\, paving the way
  for new avenues of research.
LOCATION:Seminar Room 1\, Newton Institute
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