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SUMMARY:Density Estimation in Infinite Dimensional Exponential Families - 
 Bharath Sriperumbudur (University of Cambridge)
DTSTART:20140514T100000Z
DTEND:20140514T113000Z
UID:TALK52586@talks.cam.ac.uk
CONTACT:Dr Jes Frellsen
DESCRIPTION:In this work\, we consider the problem of estimating densities
  in an infinite dimensional exponential family indexed by functions in a r
 eproducing kernel Hilbert space. Since standard techniques like maximum li
 kelihood estimation (MLE) or pseudo MLE (based on the method of sieves) do
  not yield practically useful estimators\, we propose an estimator based o
 n the minimization of Fisher divergence\, which involves solving a simple 
 finite dimensional linear system. We show that the proposed estimator is c
 onsistent\, and provide convergence rates under smoothness assumptions (pr
 ecisely\, under the assumption that the true parameter or function that ge
 nerates the data generating distribution lies in the image of a certain co
 variance operator). We also empirically demonstrate that the proposed meth
 od outperforms the standard non-parametric kernel density estimator. Joint
  work with Kenji Fukumizu\, Arthur Gretton and Aapo Hyvarinen.
LOCATION:Engineering Department\, CBL Room BE-438
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