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Can we recover meaningful spatial informa- tion from multivariate pattern analysis? Ga¨ el Varoquaux INRIA/Parietal Alexandre Gramfort Bertrand Thirion
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Can we recover meaningful spatial informa-tion from multivariate pattern analysis?
Gael Varoquaux INRIA/Parietal
AlexandreGramfort
BertrandThirion
Can we recover meaningful spatial informa-tion from multivariate pattern analysis?
Gael Varoquaux INRIA/Parietal
AlexandreGramfort
BertrandThirionYes we can!
Can we recover meaningful spatial informa-tion from multivariate pattern analysis?
Gael Varoquaux INRIA/Parietal
AlexandreGramfort
BertrandThirion
1 Prediction versus recovery
2 Random parcellations and sparsity
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?
1 Prediction versus recovery
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1 Standard analysis and MVPA
Standard analysisTest whether the voxel isrecruited by the taskMany voxels ⇒ problemof multiple comparisons
MVPAOverall predictive model
Many voxels ⇒ curse ofdimensionality
F-test SearchlightAnalyzes of regional-average activation and multi-voxel pattern information tell complementary stories,K. Jimura, R.A. Poldrack, Neuropsychologia 2011
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1 Standard analysis and MVPA
Standard analysisTest whether the voxel isrecruited by the taskMany voxels ⇒ problemof multiple comparisons
MVPAOverall predictive model
Many voxels ⇒ curse ofdimensionality
F-test SearchlightAnalyzes of regional-average activation and multi-voxel pattern information tell complementary stories,K. Jimura, R.A. Poldrack, Neuropsychologia 2011
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1 Good prediction 6=6=6= good recovery
Simple simulations: y = w X + eX: observed fMRI images: spatially smoothe: noisew: coefficients (brain regions)
Ground truth
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1 Good prediction 6=6=6= good recovery
Sparse models (lasso):Prediction: 0.78 explained variance
Amplitude of the weights:
0
max
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1 Good prediction 6=6=6= good recovery
SVM:Prediction: 0.71 explained variance
Amplitude of the weights:
0
max
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1 Good prediction 6=6=6= good recovery
Standard univariate analysis (ANOVA):
F-score:
0
max
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1 Good prediction 6=6=6= good recovery
LassoPrediction: 0.77Recovery: 0.461
SVMPrediction: 0.71Recovery: 0.464
F-scorePrediction:Recovery: 0.963
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1 Multivariate analysis for recovery?
Considering each voxel separately issuboptimal: they share information
Most often, we know that we are looking fora small fraction of the cortex
A voxel is more likely to be activatedif its neighbor is
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1 Multivariate analysis for recovery?
Considering each voxel separately issuboptimal: they share information
Most often, we know that we are looking fora small fraction of the cortex
Sparse models
A voxel is more likely to be activatedif its neighbor is
Spatial models
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1 Sparse models
Compressive sensing:detection of k signals out of p (voxels)with only n observations ∝ k
IterpretableSelects random subsets in correlated signals
Face vs housediscriminationData from [Haxby 2001]
Stability selection:Apply random perturbations to the dataKeep voxels that are selected often
[Meinhausen 2010]
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1 Sparse models
Compressive sensing:detection of k signals out of p (voxels)with only n observations ∝ k
IterpretableSelects random subsets in correlated signals
Face vs housediscriminationData from [Haxby 2001]
Stability selection:Apply random perturbations to the dataKeep voxels that are selected often
[Meinhausen 2010]
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1 Spatial models
Brain parcellations:Ward clustering to reduce voxel numbers
Supervised clustering [Michel 2011]
... ... ...
... ...
Clustering blind to experimental conditions
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2 Random parcellations andsparsity
Combining
Clustering
Sparsity
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2 Random parcellations andsparsity
+
Randomization
Stability scores
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2 Algorithm
1 loop: perturb randomly data
2 Ward agglomeration to form n features
3 sparse linear model on reduced features
4 accumulate non-zero features
5 threshold map of apparition counts
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2 Recovery performanceRandomizedClusteredLasso:
Selection scores
0
max
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2 What is the best method for feature recovery?For small brain regions: elastic netFor large brain regions: randomized-clustered sparsityLarge regions and very smooth images: F-tests
[Varoquaux 2012] ICMLG Varoquaux 13
2 fMRI: face vs house discrimination [Haxby 2001]
F-scores
L R
y=-31 x=17
L R
z=-17
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2 fMRI: face vs house discrimination [Haxby 2001]
Randomized Clustered Sparsity
L R
y=-31 x=17
L R
z=-17
Less background noise(source of false positive)
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2 Predictive power of selected voxelsObject recognition [Haxby 2001]
Using recovered voxels improves predictionG Varoquaux 15
Can we recover meaningful spatial informationfrom multivariate pattern analysis?
SVM and sparse models less powerful then F-scoreSparsity + clustering + randomization:
excellent recovery⇒ Multivariate brain mapping
Simultaneous prediction and recovery
Predictionaccuracy:93%
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For more detailsG. Varoquaux, A. Gramfort, and B. Thirion, Small-samplebrain mapping: sparse recovery on spatially correlated de-signs with randomization and clustering, ICML 2012
Acknowledgments, for sharing data:J. Haxby R. Poldrack K. Jimura
Softwarescikit-learn: machine learning in Python
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