Granger Causality on Spatial Manifolds: applications to Neuroimaging

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Granger Causality on Spatial Manifolds
applications to Neuroimaging
Pedro A. Valdés-Sosa Cuban Neuroscience Centre
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Multivariate Autoregressive Model for EEG/fMRI
t 1,,Nt
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Point influence Measures
is the simple test
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Granger Causality must be measured on a MANIFOLD
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Influence Measures defined on a Manifold
An influence field
is a multiple test
and all
for a given
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Discretization of the Continuos AR Model -I
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Multivariate Regression Formulation
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ML Estimation and detection of Influence fields
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Problemas with the Multivariate Autoregressive
Model for Brain Manifolds
t 1,,N
of parameters
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Prior Model on Influence Fields
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Priors for Influence Fields
Are of minimum norm, or maximal smoothness, etc.
Valdés-Sosa PA Neuroinformatics (2004)
21-12 Valdés-Sosa PA et al. Phil. Trans R. Soc.
B (2005) 360 969-981
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Penalty Functions
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Estimation via MM algorithm
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Penalty Covariance combinations
sparseness
smoothness
both
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Simulated fMRI
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Correlations of the EEG with the fMRI
Martinez et. al Neuroimage July 2004
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