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CATEGORIES:Statistics
SUMMARY:Functional Models for Time Varying Random Objects
- Paromita Dubey\, Stanford University
DTSTART;TZID=Europe/London:20210305T160000
DTEND;TZID=Europe/London:20210305T170000
UID:TALK155911AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/155911
DESCRIPTION:In recent years\, samples of time-varying object d
ata such as time-varying networks that are not in
a vector space have been increasingly collected. T
hese data can be viewed as elements of a general m
etric space that lacks local or global linear stru
cture and therefore common approaches that have be
en used with great success for the analysis of fun
ctional data\, such as functional principal compon
ent analysis\, cannot be applied directly.\n\nIn t
his talk\, I will propose some recent advances alo
ng this direction. First\, I will discuss ways to
obtain dominant modes of variations in time varyi
ng object data. I will describe metric covariance\
, a new association measure for paired object data
lying in a metric space (Ω\, d) that we use to de
fine a metric auto-covariance function for a sampl
e of random Ω-valued curves\, where Ω will not ha
ve a vector space or manifold structure. The propo
sed metric auto-covariance function is non-negativ
e definite when the squared metric d^2 is of negat
ive type. The eigenfunctions of the linear operato
r with the metric auto-covariance function as the
kernel can be used as building blocks for an objec
t functional principal component analysis for Ω-va
lued functional data\, including time-varying prob
ability distributions\, covariance matrices and ti
me-dynamic networks. Then I will describe how to o
btain analogues of functional principal components
for time-varying objects by applying weighted Fré
chet means which serve as projections of the rando
m object trajectories in the directions of the eig
enfunctions\, leading to Ω-valued Fréchet integral
s. \n\nThis talk is based on joint work with Hans-
Georg Müller.
LOCATION: https://maths-cam-ac-uk.zoom.us/j/92821218455?pwd
=aHFOZWw5bzVReUNYR2d5OWc1Tk15Zz09
CONTACT:Dr Sergio Bacallado
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