Predictive Modeling of Spatial Properties of fMRI Response Predictive Modeling of Spatial Properties of fMRI Response Melissa K. Carroll Princeton University Pace Gargano Research Day May 8, 2009

Acknowledgements IBM Guillermo Cecchi Guillermo Cecchi Irina Rish Irina Rish Rahul Garg Rahul Garg Ravi Rao Ravi Rao Princeton and Beyond Rob Schapire Rob Schapire Ken Norman Ken Norman Jim Haxby (Dartmouth) Jim Haxby (Dartmouth)

Blood Oxygenation Level Dependent Response (BOLD) FMRIB, Oxford Oxygenation level response over time: Increased ratio oxygenated to deoxygenated hemoglobin nearby: Neural activity:

Functional Magnetic Resonance Imaging (fMRI) 1 voxel (~2-3 mm 3 ) 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 Blurring Temporal: hemodynamic response lag Temporal: hemodynamic response lag Spatial: voxels are arbitrary discretizations Spatial: voxels are arbitrary discretizations Neural response diffusedNeural response diffused millions of neurons within voxel millions of neurons within voxel larger regions often share response larger regions often share response Diffuse vascular hemodynamic responseDiffuse vascular hemodynamic response Spread over several voxels Spread over several voxels ShiftingShifting Head movement throughout experiment Head movement throughout experiment If combining across subjects, brain size and shape differences If combining across subjects, brain size and shape differences Effect: strong voxel auto-correlationEffect: strong voxel auto-correlation

Cognitive State Classification (MVPA) Brain Scan Object Viewed Time Time 1 Time 2 Time 3 Time X … Images: J. Haxby

Model Reliability and Interpretation Observed: Observed: Voxel “relevance” different between models trained on different data subsetsVoxel “relevance” different between models trained on different data subsets e.g. two “runs” of same experiment e.g. two “runs” of same experiment Should we care? Maybe: Should we care? Maybe: Interpretation: if model can reliably predict, what is the common pattern of activity?Interpretation: if model can reliably predict, what is the common pattern of activity? Representation: perhaps voxel is wrong unit to model and could further improve predictionRepresentation: perhaps voxel is wrong unit to model and could further improve prediction

Sparse Regression for MVPA Linear regression formulation: Linear regression formulation: solve for fMRI volume predicted response (continuous) PROBLEM: too many predictors (voxels): ~30,000 solutions are overfit to data: poor generalization difficult to interpret (determine relevant voxels) SOLUTION: sparse regression include only relevant voxels in model LASSO: add ℓ 1 -regularization: most β weights become 0 βx = y

Reliability Problem: LASSO and Correlated Predictors ℓ 1 Pure ℓ 1 (LASSO)Truth relevant cluster of correlated predictors

Elastic Net: Compromise Between ℓ 1 and ℓ 2 to Improve Reliability Zou and Hastie, 2005 ridge penalty λ 2 elastic net penalty lasso penalty λ 1

Elastic Net for MVPA Goal: use Elastic Net to predict continuous cognitive states from fMRI Goal: use Elastic Net to predict continuous cognitive states from fMRI Known: increasing λ 2 should increase inclusion of correlated voxels Known: increasing λ 2 should increase inclusion of correlated voxels Hypotheses Hypotheses Greater inclusion of correlated voxels Greater inclusion of correlated voxels  greater reliability across data subsets (experimental runs) greater reliability across data subsets (experimental runs) larger spatially localized clusters larger spatially localized clusters not necessarily improved prediction performance not necessarily improved prediction performance Carroll et al., Neuroimage, 2009

Overall 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 λ 2 parameter

Increased λ 2  Increased Robustness (Part 1) As λ 2 is increased… Prediction performance stays the same for all responses… and though more voxels are used…

Increased λ 2  Increased Robustness (Part 2) Robustness is significantly improved Robustness is significantly improved Additional voxels are the relevant but redundant voxels Additional voxels are the relevant but redundant voxels

Fewer, More Localized Clusters λ 2 = 0.1λ 2 = 2.0 Subject 1, Run 1, Instructions response

Conclusions Sparse models can improve prediction and interpretation for fMRI data Sparse models can improve prediction and interpretation for fMRI data Model reliability can be improved even among equally well-predicting models Model reliability can be improved even among equally well-predicting models More reliable MVPA models reveal distributed clusters of localized activity More reliable MVPA models reveal distributed clusters of localized activity Still large room for improvement in reliability Still large room for improvement in reliability