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SUMMARY:From scattered samples to fields of distributions: theory and prac
 tice of Spatial Logistic Gaussian Processes - Athénaïs  Gautier (ONERA)
DTSTART:20250701T093000Z
DTEND:20250701T103000Z
UID:TALK233533@talks.cam.ac.uk
DESCRIPTION:Spatial Logistic Gaussian Processes (SLGPs) offer a probabilis
 tic framework for modelling random fields of probability measures indexed 
 by arbitrary covariates. Constructed by applying a non-linear transformati
 on to a latent Gaussian Process\, SLGPs are models flexible enough to enco
 de complex variations in shape and modality. Crucially\, they enable proba
 bilistic inference in settings with scattered\, irregularly spaced\, or no
 n-replicated data.\nThis talk explores both theoretical and practical cont
 ributions. On the theoretical side\, we formalise SLGPs as representers of
  random probability measure fields and investigate their structure and smo
 othness properties. We extend classical spatial statistics notions such as
  expected mean-square continuity to the distributional setting\, and we es
 tablish sufficient conditions on the covariance kernel of the underlying G
 P to ensure spatial regularity with respect to statistical dissimilarities
  between distributions (e.g.\, Hellinger\, KL\, total variation).From a pr
 actical perspective\, we introduce an implementation based on finite-rank 
 approximations using Random Fourier Features\, and propose several inferen
 ce schemes&mdash\;MCMC\, MAP\, and Laplace approximation&mdash\;each balan
 cing statistical fidelity and computational cost. We illustrate the flexib
 ility and expressiveness of the SLGP models through experiments on synthet
 ic and real-world datasets\, including challenging non-replicated and hete
 rogeneously sampled settings.&nbsp\;
LOCATION:Seminar Room 2\, Newton Institute
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