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