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Theses

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. Beside 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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https://tel.archives-ouvertes.fr/tel-03223096
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Submitted on : Wednesday, September 22, 2021 - 9:56:12 AM
Last modification on : Thursday, March 24, 2022 - 3:42:41 AM
Long-term archiving on: : Thursday, December 23, 2021 - 6:02:04 PM

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Ayoub Belhadji. Subspace sampling using determinantal point processes.. Automatic Control Engineering. Centrale Lille Institut, 2020. English. ⟨NNT : 2020CLIL0021⟩. ⟨tel-03223096⟩

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