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SUMMARY:Procrustes Analysis of Covariance Operators and Optimal Transport 
 of Gaussian Processes - Victor Panaretos (EPFL - Ecole Polytechnique Féd
 érale de Lausanne)
DTSTART:20180319T100000Z
DTEND:20180319T110000Z
UID:TALK102562@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Covariance operators are fundamental in functional data analys
 is\, providing the canonical means to analyse functional variation via the
  celebrated Karhunen-Lo&egrave\;ve expansion. These operators may themselv
 es be subject to variation\, for instance in contexts where multiple funct
 ional populations are to be compared. Statistical techniques to analyse su
 ch variation are intimately linked with the choice of metric on covariance
  operators\, and the intrinsic infinite-dimensionality of these operators.
  We will describe the manifold-like geometry of the space of trace-class i
 nfinite-dimensional covariance operators and associated key statistical pr
 operties\, under the recently proposed infinite-dimensional version of the
  Procrustes metric. In particular\, we will identify this space with that 
 of centred Gaussian processes equipped with the Wasserstein metric of opti
 mal transportation. The identification allows us to provide a description 
 of those aspects of the geometry that are important in terms of statistica
 l inference\, and establish key properties of the Fr&eacute\;chet mean of 
 a random sample of covariances\, as well as generative models that are can
 onical for such metrics. The latter will allow us to draw connections with
  the problem of registration of warped functional data. Based on joint wor
 k with V. Masarotto (EPFL) and Y. Zemel (G&ouml\;ttingen).
LOCATION:Seminar Room 1\, Newton Institute
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