Sparse space-time models: Concentration Inequalities and Lasso

Guilherme Ost; Patricia Reynaud-Bouret

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arXiv · 1807.07615

Sparse space-time models: Concentration Inequalities and Lasso

Guilherme Ost·Patricia Reynaud-Bouret

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Abstract

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 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.

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Guilherme Ost, Patricia Reynaud-Bouret. 2018-07-19. Sparse space-time models: Concentration Inequalities and Lasso. https://arxiv.org/abs/1807.07615

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