Predictive Modeling of Spatial Properties of fMRI Response

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

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

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

4. Functional Magnetic Resonance Imaging (fMRI) 1 “TR” =1 3D image (~1 per 2 sec) 1 voxel (~2-3 mm3) One fMRI “time to response” volume: measure of BOLD response at given time

5. BOLD: Spatio-Temporal Blurring Temporal: hemodynamic response lag Spatial: voxels are arbitrary discretizations Neural response diffused millions of neurons within voxel larger regions often share response Diffuse vascular hemodynamic response Spread over several voxels Shifting Head movement throughout experiment If combining across subjects, brain size and shape differences Effect: strong voxel auto-correlation

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

7. Model Reliability and Interpretation Observed: Voxel “relevance” different between models trained on different data subsets e.g. two “runs” of same experiment Should we care? Maybe: 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 prediction

8. Sparse Regression for MVPA βx = y 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 ℓ1-regularization: • most β weights become 0 Linear regression formulation:

9. Reliability Problem: LASSO and Correlated Predictors Truth Pure ℓ1 (LASSO) relevantcluster of correlated predictors

10. Elastic Net: Compromise Between ℓ1 and ℓ2 to Improve Reliability ridge penaltyλ2 elastic net penalty lasso penaltyλ1 Zou and Hastie, 2005

11. Elastic Net for MVPA • Goal: use Elastic Net to predict continuous cognitive states from fMRI • Known: increasing λ2 should increase inclusion of correlated voxels • Hypotheses • Greater inclusion of correlated voxels  • greater reliability across data subsets (experimental runs) • larger spatially localized clusters • not necessarily improved prediction performance Carroll et al., Neuroimage, 2009

12. Overall Prediction Performance Sparse methods > non-sparse methods, but similar to each other λ2 parameter Averaged over 3 subjects, 24 response vectors, 2 runs, and 4 cross-validation folds

13. Increased λ2  Increased Robustness (Part 1) As λ2 is increased… Prediction performance stays the same for all responses… and though more voxels are used…

14. Increased λ2  Increased Robustness (Part 2) • Robustness is significantly improved • Additional voxels are the relevant but redundant voxels

15. Fewer, More Localized Clusters Subject 1, Run 1, Instructions response λ2 = 0.1 λ2 = 2.0

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