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Subspace sampling using determinantal point processes

Abstract : Determinantal point processes are probabilistic models of repulsion. These models were studied in various fields: random matrices, quantum optics, spatial statistics, image processing, machine learning, and recently numerical integration. In this thesis, we study subspace sampling using determinantal point processes. This problem takes place within the intersection of three sub-domains of approximation theory: subset selection, kernel quadrature, and kernel interpolation. We study these classical topics, through a new interpretation of these probabilistic models: a determinantal point process is a natural way to define a random subspace. Besides giving a unified analysis to numerical integration and interpolation under determinantal point processes, this new perspective allows to work out the theoretical guarantees of several approximation algorithms and to prove their optimality in some settings.
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Contributor : Ayoub Belhadji Connect in order to contact the contributor
Submitted on : Friday, May 14, 2021 - 4:13:29 PM
Last modification on : Tuesday, January 4, 2022 - 6:12:48 AM


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  • HAL Id : tel-03149292, version 2



Ayoub Belhadji. Subspace sampling using determinantal point processes. Mathematics [math]. Ecole Centrale de Lille, 2020. English. ⟨tel-03149292v2⟩



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