Can we recover meaning full spatial information from multivariate pattern analysis

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:

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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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