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SUMMARY:PCA for point processes
DTSTART:20250707T080500Z
DTEND:20250707T083500Z
DTSTAMP:20260423T021500Z
UID:indico-event-14490@indico.math.cnrs.fr
DESCRIPTION:Speakers: Vincent Rivoirard\n\nWe introduce a novel statistica
 l framework for the analysis of replicated point processes that allows for
  the study of point pattern variability at a population level. By treating
  point process realizations as random measures\, we adopt a functional ana
 lysis perspective and propose a form of functional Principal Component Ana
 lysis (fPCA) for point processes. The originality of our method is to base
  our analysis on the cumulative mass functions of the random measures whic
 h gives us a direct and interpretable analysis. Key theoretical contributi
 ons include establishing a Karhunen-Loève expansion for the random measur
 es and a Mercer Theorem for covariance measures. We establish convergence 
 in a strong sense\, and introduce the concept of principal measures\, whic
 h can be seen as latent processes governing the dynamics of the observed p
 oint patterns. We propose an easy-to-implement estimation strategy of eige
 nelements for which parametric rates are achieved. We fully characterize t
 he solutions of our approach to Poisson and Hawkes processes and validate 
 our methodology via simulations and diverse applications in seismology\, s
 ingle-cell biology and neurosiences\, demonstrating its versatility and ef
 fectiveness. Joint work with Victor Panaretos (EPFL)\, Franck Picard (ENS 
 de Lyon) and Angelina Roche (Université Paris Cité). \n\nhttps://indico
 .math.cnrs.fr/event/14490/
URL:https://indico.math.cnrs.fr/event/14490/
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