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SUMMARY:Functional Models for Time Varying Random Objects - Paromita Dubey
 \, Stanford University
DTSTART:20210305T160000Z
DTEND:20210305T170000Z
UID:TALK155911@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:In recent years\, samples of time-varying object data such as 
 time-varying networks that are not in a vector space have been increasingl
 y collected. These data can be viewed as elements of a general metric spac
 e that lacks local or global linear structure and therefore common approac
 hes that have been used with great success for the analysis of functional 
 data\, such as functional principal component analysis\, cannot be applied
  directly.\n\nIn this talk\, I will propose some recent advances along thi
 s direction.  First\, I will discuss ways to obtain dominant modes of vari
 ations in time varying 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 define a metric auto-covariance function for a sample
  of random  Ω-valued curves\, where Ω will not have a vector space or ma
 nifold structure. The proposed metric auto-covariance function is non-nega
 tive definite when the squared metric d^2 is of negative type. The eigenfu
 nctions of the linear operator with the metric auto-covariance function as
  the kernel can be used as building blocks for an object functional princi
 pal component analysis for Ω-valued functional data\, including time-vary
 ing probability distributions\, covariance matrices and time-dynamic netwo
 rks. Then I will describe how to obtain analogues of functional principal 
 components for time-varying objects by applying weighted Fréchet means wh
 ich serve as projections of the random object trajectories in the directio
 ns of the eigenfunctions\, leading to Ω-valued Fréchet integrals. \n\nTh
 is talk is based on joint work with Hans-Georg Müller.
LOCATION: https://maths-cam-ac-uk.zoom.us/j/92821218455?pwd=aHFOZWw5bzVReU
 NYR2d5OWc1Tk15Zz09
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