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Estimation of local dependence graphs via Hawkes processes and link with functional connectivity in neurosciences

Patricia Bouret,

Date and Time: Dec 02, 2013 (10:00 AM)
Location: Orchard room (3280) at the Wisconsin Institute for Discovery Building

Abstract:

Due to its low computational cost, Lasso is an attractive
regularization method for high-dimensional statistical settings. In
this paper, we consider multivariate counting processes depending on
an unknown function parameter to be estimated by linear combinations
of a fixed dictionary. To select coefficients, we propose an adaptive
$\ell_1$-penalization methodology, where data-driven weights of the
penalty are derived from new Bernstein type inequalities for
martingales. Oracle inequalities are established under assumptions on
the Gram matrix of the dictionary. This method is then applied to
Hawkes processes as model for spike train analysis. The estimation
allows us to recover the functional underlying connectivity as the
local dependence graph that has been estimated. Simulations and real
data analysis show the excellent performances of our method in
practice.

This is a joint work (still in progress) with V. Rivoirard (Dauphine),
C. Tuleau-Malot, F. Grammont (Nice), N.R. Hansen (Copenhagen), T.
Bessaih, R. Lambert, N. Leresche (Paris 6).