Graphical models of brain function across individuals
35 Pages
English
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Graphical models of brain function across individuals

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Gain access to the library to view online
Learn more
35 Pages
English

Description

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


Subjects

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Language English
Document size 7 MB

Exrait

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