Graphical models of brain function across individuals

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Graphical models of brain function across individuals Gael Varoquaux INSERM U992, Unicog INRIA, Parietal Joint work with: Bertrand Thirion Andreas Kleinschmidt Alexandre Gramfort Pierre Fillard

inter-subjects modeling

neural networks

functional brain

function across

elegans neural

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Publié par

profil-urra-2012

Nombre de lectures

Langue

English

Poids de l'ouvrage

7 Mo

Kleinschmidt Institut national de la santé et de la recherche médicale Neural network (disambiguation)

Graphical models of brain function
across individuals
Ga¨el Varoquaux
INSERM U992, Unicog
INRIA, Parietal
Joint work with:
Bertrand Thirion
Andreas Kleinschmidt
Alexandre Gramfort
Pierre FillardNeural networks
[Watts and Strogatz 1998]
Small world properties in
C. Elegans neural network
Human brain:
11 1610 neurons, 10 synapses
G Varoquaux 2Functional brain imaging
50 000 voxels,
300 time points
G Varoquaux 3Functional connectivity and graphical models
Modeling the correlation
structure of ongoing activity
G Varoquaux 4Inter-subjects modeling
Discriminative information between
subjects
Diagnostic or prognostic information?
Better models of brain function
Accumulating data in a population
G Varoquaux 5Presentation outline
1 Detecting diﬀerences in connectivity
2 Individual models with population data
G Varoquaux 61 Detecting diﬀerences in
connectivity
Functional markers on diminished patients?
Stroke outcome prognosis in ongoing activity
??
⇔
?
G Varoquaux 71 Failure of univariate approach on correlations
Subject variability spread across correlation matrices
Control Control Control Large lesion
dΣ = Σ − Σ is not deﬁnite positive2 1
⇒ contradictory with Gaussian models
Σ does not live in a vector space
G Varoquaux 8
100205251001515205251020201525105515025251520515251015255002025102001520101050051 Simulation on a toy problem
Simulate two processes with diﬀerent inverse covariance
K : K − K : Σ : Σ − Σ :1 1 2 1 1 2
Add jitter in observed covariance... sample
MSE(K − K ): MSE(Σ − Σ ):1 2 1 2
Non-local eﬀects and non homogeneous noise
G Varoquaux 91 Theoretical settings: comparison of estimates
1 2Observations in 2 populations: X and X
1 1^ ^Goal: comparing estimates: θ(X ) and θ(X )

1 1 1 −1^Asymptotic normality: θ(X )∼N θ , I(θ )
-1 θ²( )θ²I
-1
( )θ¹Iθ¹
G Varoquaux 10