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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20220421T103720Z
DTSTART:20220427T140000Z
DTEND:20220427T150000Z
SUMMARY:Mikolaj Kasprzak - Stein's method and Gaussian process approxima
tions
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}l1kk-l28vdj
v7-d5ugkc
DESCRIPTION:Mikolaj Kasprzak (University of Luxembourg) will speak in the
Probability seminar. \n\nFunctional limit theorems have found multiple
applications in fields ranging from statistical changepoint detection to
probabilistic population genetics. In the field of machine learning\, a
nalysing Gaussian processes arising as functional limits of stochastic g
radient algorithms has recently been proposed as a method to approximate
ly compute their mixing times and averaged-process distributions. Howeve
r\, functional approximations are rarely equipped with theoretical guara
ntees on their quality\, which limits their practical applicability. At
the same time\, Gaussian processes are commonly applied as models in num
erous areas\, including that of functional data analysis. Unfortunately\
, tools for testing goodness of fit to Gaussian processes are not widely
available in the litarature\, which makes functional data analysts unab
le to accurately assess how good their modelling choices are. \n\nIn thi
s talk\, I will present results (proved using Stein's method) which can
be considered as initial steps towards building a theory for quantifying
the error in functional Gaussian process approximations. I will show ho
w those initial results may be used to analyse the rate of functional co
nvergence of sequences of weighted U-statistics. I will also talk about
an upcoming work on Gaussian Process goodness-of-fit testing using Stein
's method on Hilbert spaces and its applicability to functional data ana
lysis problems. On the theoretical side\, I will describe different ways
in which one can use Stein's method in the context of infinite-dimensio
nal distributions and build infinite-dimensional Stein discrepancies.\n\
nThe talk will be based on multiple results obtained together with Chris
tian DÃ¶bler\, Andrew Duncan\, Giovanni Peccati and George Wynne.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:https://zoom.us/j/95434478825
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