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Predictive Modeling of Spatial PrPredictive Modeling of Spatial Properties of operties of
fMRIfMRI Response Response Melissa K. CarrollMelissa K. Carroll
Princeton UniversityPrinceton University
Pace Gargano Research DayPace Gargano Research DayMay 8, 2009May 8, 2009
AcknowledgementsAcknowledgements
IBMIBM Guillermo CecchiGuillermo Cecchi Irina RishIrina Rish Rahul GargRahul Garg Ravi RaoRavi Rao
Princeton and BeyondPrinceton and Beyond Rob SchapireRob Schapire Ken NormanKen Norman Jim Haxby Jim Haxby
(Dartmouth)(Dartmouth)
Blood Oxygenation Level Blood Oxygenation Level Dependent Response (BOLD)Dependent Response (BOLD)
FMRIB, Oxford
Oxygenation level response over time:
Increased ratio oxygenated to deoxygenated hemoglobin nearby:
Neural activity:
Functional Magnetic Resonance Functional Magnetic Resonance Imaging (fMRI)Imaging (fMRI)
1 voxel(~2-3 mm3)
1 “TR” =1 3D image(~1 per 2 sec)
One fMRI “time to response” volume: measure of BOLD response at given time
BOLD: Spatio-Temporal BOLD: Spatio-Temporal BlurringBlurring
TemporalTemporal: hemodynamic response lag: hemodynamic response lag Spatial: Spatial: voxels are arbitrary discretizationsvoxels are arbitrary discretizations
• Neural response diffusedNeural response diffused millions of neurons within voxelmillions of neurons within voxel larger regions often share responselarger regions often share response
• Diffuse vascular hemodynamic responseDiffuse vascular hemodynamic response Spread over several voxelsSpread over several voxels
• ShiftingShifting Head movement throughout experimentHead movement throughout experiment If combining across subjects, brain size and shape If combining across subjects, brain size and shape
differencesdifferences
• Effect: strong voxel auto-correlationEffect: strong voxel auto-correlation
Cognitive State Classification Cognitive State Classification (MVPA)(MVPA)
Brain Scan
Object Viewed
Time
Time 1 Time 2 Time 3 Time X
…
Images: J. Haxby
Model Reliability and InterpretationModel Reliability and Interpretation
Observed:Observed:• Voxel “relevance” different between Voxel “relevance” different between
models trained on different data subsetsmodels trained on different data subsets e.g. two “runs” of same experimente.g. two “runs” of same experiment
Should we care? Maybe:Should we care? Maybe:• Interpretation:Interpretation: if model can reliably predict, if model can reliably predict,
what is the common pattern of activity?what is the common pattern of activity?• Representation:Representation: perhaps voxel is wrong unit perhaps voxel is wrong unit
to model and could further improve to model and could further improve predictionprediction
Sparse Regression for MVPASparse Regression for MVPA Linear regression formulation:Linear regression formulation:
solve for
fMRI volume
predicted response (continuous)
PROBLEM: PROBLEM: too many predictors (voxels): ~30,000too many predictors (voxels): ~30,000
solutions are solutions are overfitoverfit to data: poor generalization to data: poor generalization
difficult to difficult to interpretinterpret (determine relevant voxels) (determine relevant voxels)
SOLUTION: SOLUTION: sparse regressionsparse regression
include only relevant voxels in modelinclude only relevant voxels in model
LASSO: LASSO: add ℓadd ℓ11-regularization: -regularization:
most most ββ weights become 0 weights become 0
βx = y
Reliability Problem: LASSO and Reliability Problem: LASSO and Correlated PredictorsCorrelated Predictors
Pure ℓℓ11 (LASSO)Truthrelevantcluster of correlated predictors
Elastic Net: Compromise Between Elastic Net: Compromise Between ℓℓ11 and ℓ and ℓ22 to Improve Reliability to Improve Reliability
Zou and Hastie, 2005
ridge penaltyλ2
elastic net penalty
lasso penaltyλ1
Elastic Net for MVPAElastic Net for MVPA
Goal: use Elastic Net to predict continuous Goal: use Elastic Net to predict continuous cognitive states from fMRIcognitive states from fMRI
Known: increasing Known: increasing λλ22 should increase inclusion should increase inclusion of correlated voxelsof correlated voxels
HypothesesHypotheses• Greater inclusion of correlated voxels Greater inclusion of correlated voxels
greater reliability across data subsets greater reliability across data subsets (experimental runs)(experimental runs)
larger spatially localized clusterslarger spatially localized clusters not necessarily improved prediction performancenot necessarily improved prediction performance
Carroll et al., Neuroimage, 2009
Overall Prediction PerformanceOverall Prediction Performance
Sparse methods > non-sparse methods, but similar to each other
Averaged over 3 subjects, 24 response vectors, 2 runs, and 4 cross-validation folds
λ2 parameter
Increased Increased λλ2 2 Increased Increased
Robustness (Part 1)Robustness (Part 1)As λ2 is increased…
Prediction performance stays the same for all responses…
and though more voxels are used…
Increased Increased λλ2 2 Increased Increased
Robustness (Part 2)Robustness (Part 2) Robustness is Robustness is
significantly significantly improvedimproved
Additional Additional voxels are the voxels are the relevant but relevant but redundant redundant voxelsvoxels
Fewer, More Localized ClustersFewer, More Localized Clusters
λ2 = 0.1 λ2 = 2.0
Subject 1, Run 1, Instructions response
ConclusionsConclusions
Sparse models can improve prediction and Sparse models can improve prediction and interpretation for fMRI datainterpretation for fMRI data
Model reliability can be improved even Model reliability can be improved even among equally well-predicting modelsamong equally well-predicting models
More reliable MVPA models reveal More reliable MVPA models reveal distributed clusters of distributed clusters of localizedlocalized activity activity
Still large room for improvement in Still large room for improvement in reliabilityreliability