Sparse space-time models: Concentration Inequalities and Lasso


Guilherme Ost (UFRJ)


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24 de Setembro de 2020, às 16h

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 eigenvalue properties for the associated Gram matrix with high probability. These results hold even if the network is only partially observed. The main argument relies on the fact that concentration inequalities can easily be derived whenever the transition probabilities of the underlying process admit a sparse space-time representation..

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Guilherme Ost is an assistant Professor of the IM-UFRJ, the Institute of Mathematics of the Federal University of Rio de Janeiro. He obtained his Ph.D. in Statistics (2015) from University of São Paulo, under the supervision of Antônio Galves. He took a one-year post-doc (Dec 2015 - Dec 2016at Université de Cergy-Pontoise under supervision of Eva Löcherbach. Afterwards worked as post-doc fellow (Dec 2016 - Fev 2018) at RIDC NeuroMat (IME-USP) under the supervision of Pablo Ferrari.His research interests are high-dimensinal probability and statistics, mean field limits and stochastic modeling in neuroscience.