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Archive / INF Seminars / INF_2025_01_30_VincentRivoirard

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	PCA for point processes

Host: Igor Pivkin, Prof. Deborah Sulem

Thursday

30.01

USI East Campus, Room D5.01

12:00 - 13:30


	Vincent Rivoirard University Paris Dauphine

Abstract: We introduce a novel statistical 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 analysis perspective and propose a form of functional Principal Component Analysis (fPCA) for point processes. The originality of our method is to base our analysis on the cumulative mass functions of the random measures which gives us a direct and interpretable analysis. Key theoretical contributions include establishing a Karhunen-Loève expansion for the random measures and a Mercer Theorem for covariance measures. We establish convergence in a strong sense, and introduce the concept of principal measures, which can be seen as latent processes governing the dynamics of the observed point patterns. We propose an easy-to-implement estimation strategy of eigenelements for which parametric rates are achieved. We fully characterize the solutions of our approach to Poisson and Hawkes processes and validate our methodology via simulations and diverse applications in seismology, single-cell biology and neurosiences, demonstrating its versatility and effectiveness.

Biography: Vincent Rivoirard has been Professor at the University Paris Dauphine since 2010 after having been Associate Professor at the University of Paris Sud Orsay between 2003 and 2010. He defended his thesis in statistics in 2002 under the supervision of Dominique Picard. His research interests cover non-parametric and high dimension statistics for Bayesian and frequentist estimation. He is interested in statistical applications in neuroscience, genetics and biology. He was Director of Ceremade between November 1, 2016 and December 31, 2022