HETEROGENEOUS MULTISCALE MULTIVARIATE AUTOREGRESSIVE MODEL: EXISTENCE, SPARSE ESTIMATION AND APPLICATION TO FUNCTIONAL CONNECTIVITY IN NEUROSCIENCE

Spaziani Stefano (1) , Girardeau Gabrielle (2) , Bethus Ingrid (3) , Reynaud-Bouret Patricia (1)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 IFM - Inserm U1270 - SU - Institut du Fer à Moulin
3 IPMC - Institut de pharmacologie moléculaire et cellulaire

In neuroscience, functional connectivity can be seen as a graph of interactions between brain oscillations rhythms and individual neuronal activity. This graph is associated with a cognitive state and helps understand high-cognitive processes such as learning. However, up to our knowledge, there is no model nor method to assess at once directed interactions between all these heterogeneous multiscale data. In this article, we propose a new model called HM-MVAR (Heterogeneous Multiscale Multivariate Autoregressive) to represent linear combinations of classic interaction patterns such as phase-locking or power-triggered phenomena. Because of the multiscale structure, we use a block version of stationarity to exhibit conditions under which the corresponding process exists and is stationary. We also propose a data-driven weighted LASSO estimator based on martingale exponential deviation in equalities that may have an interest per se. We prove that our estimator satisfies an oracle inequality and we show its good performance on realistic simulations. Finally, when applying it on a publicly available multiscale data set from the Buzsaki Lab, we recover interactions described in the literature but also uncover new phenomena of potential interest.

Mots clés: MSC2020 subject classifications: Primary 62M10 62P10; secondary 62G05 62H12 60G10 Autoregressive process Hawkes process LASSO estimator Multiscale approach Functional connectivity Wavelet; MSC2020 subject classifications: Primary 62M10; 62P10; secondary 62G05; 62H12; 60G10 Autoregressive process; Hawkes process; LASSO estimator; Multiscale approach; Functional connectivity; Wavelet

Domaines: Statistiques [stat]

Spaziani Stefano, Girardeau Gabrielle, Bethus Ingrid, Reynaud-Bouret Patricia. HETEROGENEOUS MULTISCALE MULTIVARIATE AUTOREGRESSIVE MODEL: EXISTENCE, SPARSE ESTIMATION AND APPLICATION TO FUNCTIONAL CONNECTIVITY IN NEUROSCIENCE. Annals of Statistics, inPress. ⟨hal-04177624⟩