SPARSE SPACE-TIME MODELS: CONCENTRATION INEQUALITIES AND LASSO

Creators: Ost, G; Reynaud-Bouret, Patricia

Others:: Universidade Federal do Rio de Janeiro (UFRJ); Laboratoire Jean Alexandre Dieudonné (JAD) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA); NeuroMod InstituteFAPESP Research, Innovation and Dissemination Center for Neuromathematics (grant 2013/07699- 0); ANR-15-IDEX-0001,UCA JEDI,Idex UCA JEDI(2015); ANR-19-P3IA-0002,3IA@cote d'azur,3IA Côte d'Azur(2019)

Description

Inspired by Kalikow-type decompositions, we introduce a new stochastic model of infinite neuronal networks, for which we establish sharp oracle inequalities for Lasso methods and restricted eigen-value properties for the associated Gram matrix with high probability. These results hold even if the network is only partially observed. The main argument rely on the fact that concentration inequalities can easily be derived whenever the transition probabilities of the underlying process admit a sparse space-time representation.

Abstract

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SPARSE SPACE-TIME MODELS: CONCENTRATION INEQUALITIES AND LASSO

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Abstract

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