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SUMMARY:A statistical framework for analyzing shape in a time series of ra
 ndom geometric objects
DTSTART:20231215T151500
DTEND:20231215T170000
DTSTAMP:20260407T002953Z
UID:99a67c5c8d0d70c01a5b2b1fe9c8904c0635e8fa3afd247fb362e52a
CATEGORIES:Conferences - Seminars
DESCRIPTION:Anne van Delft\, Columbia University\nWe introduce a new  fra
 mework to analyze shape descriptors that capture the geometric features of
  an ensemble of point clouds. At the core of our approach is the point of 
 view that the data arises as sampled recordings from a metric space-valued
  stochastic process\, possibly of nonstationary nature\, thereby integrati
 ng geometric data analysis into the realm of functional time series analys
 is. We focus on the descriptors coming from topological data analysis. Our
  framework allows for natural incorporation of spatial-temporal dynamics\,
  heterogeneous sampling\, and the study of convergence rates. Further\, we
   derive  complete invariants for classes of metric space-valued stochas
 tic processes in the spirit of Gromov\, and relate these invariants to so-
 called ball volume processes.\nUnder mild dependence conditions\, a weak i
 nvariance principle in $D([0\,1]\\times [0\,\\mathscr{R}])$ is established
  for sequential empirical versions of the latter\, assuming the probabilis
 tic structure possibly  changes over time. Finally\, we use this result t
 o introduce novel test statistics for topological change\, which are distr
 ibution free in the limit under the hypothesis of stationarity.\nhttps://a
 rxiv.org/pdf/2304.01984.pdf\n\n (joint work with Andrew J. Blumberg)\n\n
  
LOCATION:MA A3 31 https://plan.epfl.ch/?room==MA%20A3%2031
STATUS:CONFIRMED
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