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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Procrustes Analysis of Covariance Operators and Op
timal Transport of Gaussian Processes - Victor Pan
aretos (EPFL - Ecole Polytechnique Fédérale de Lau
sanne)
DTSTART;TZID=Europe/London:20180319T100000
DTEND;TZID=Europe/London:20180319T110000
UID:TALK102562AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/102562
DESCRIPTION:Covariance operators are fundamental in functional
data analysis\, providing the canonical means to
analyse functional variation via the celebrated Ka
rhunen-Loè\;ve expansion. These operators ma
y themselves be subject to variation\, for instanc
e in contexts where multiple functional population
s are to be compared. Statistical techniques to an
alyse such variation are intimately linked with th
e choice of metric on covariance operators\, and t
he intrinsic infinite-dimensionality of these oper
ators. We will describe the manifold-like geometry
of the space of trace-class infinite-dimensional
covariance operators and associated key statistica
l properties\, under the recently proposed infinit
e-dimensional version of the Procrustes metric. In
particular\, we will identify this space with tha
t of centred Gaussian processes equipped with the
Wasserstein metric of optimal transportation. The
identification allows us to provide a description
of those aspects of the geometry that are importan
t in terms of statistical inference\, and establis
h key properties of the Fré\;chet mean of a
random sample of covariances\, as well as generati
ve models that are canonical for such metrics. The
latter will allow us to draw connections with the
problem of registration of warped functional data
. Based on joint work with V. Masarotto (EPFL) and
Y. Zemel (Gö\;ttingen).
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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