170 likes | 347 Views
Granger Causality on Spatial Manifolds: applications to Neuroimaging. Pedro A. Valdés-Sosa Cuban Neuroscience Centre. Multivariate Autoregressive Model for EEG/fMRI. 1 2 … p. …. t =1,…,N. t t-1. t =1,…,Nt. Point influence Measures. is the simple test.
E N D
Granger Causality on Spatial Manifolds: applications to Neuroimaging Pedro A. Valdés-Sosa Cuban Neuroscience Centre
Multivariate Autoregressive Model for EEG/fMRI 1 2 … p … t =1,…,N t t-1 t =1,…,Nt
Point influence Measures is the simple test
Influence Measures defined on a Manifold An influence field is a multiple test for a given and all
Problemas with the Multivariate Autoregressive Model for Brain Manifolds p→∞ t =1,…,N # of parameters
Priors for Influence Fields Are of minimum norm, or maximal smoothness, etc. Valdés-Sosa PA Neuroinformatics (2004) 2:1-12 Valdés-Sosa PA et al. Phil. Trans R. Soc. B (2005) 360: 969-981
Penalty Covariance combinations Model Name in statistics Known as to wavleteers as LASSO Basis Pursuit Ridge Frames Data Fusion Spline (“LORETA”) Elastic Net Fused Lasso “Ridge Fusion” ? sparseness smoothness both
Correlations of the EEG with the fMRI Martinez et. al Neuroimage July 2004