Neuroimaging for Machine Learners Validation and inference

1. Neuroimaging for Machine LearnersValidation and inference PRoNTo course May 2012 Christophe Phillips Cyclotron Research Centre, ULg, Belgium http://www.cyclotron.ulg.ac.be

2. Introduction • Within vs. between subjects analysis • GLM and contrasts • Statistical inference • Multiple comparison problem • Other inference levels • Conclusion

4. Standard Statistical Analysis (encoding) Input Output Standard univariate approach ... Voxel-wise GLM model estimation Correction for multiple comparisons Independent statistical test at each voxel BOLD signal Univariate statistical Parametric map Time Find the mappinggfrom explanatory variableXto observed dataY g: X  Y

5. Within vs. between subjects Within subject analysis: • data = functional MRI (fMRI) • modelling BOLD response time series, usually activation task • sometimes with parametric modulation and/or confounding regressor • « first level » analysis • output = raw signal, contrast images and statistical maps

6. Within vs. between subjects Between subjects analysis: • data = tissue probability, deformation map, contrast image, FDG-PET scan,… • modelling group differences or regressing subjects’ score (confound/interest) • « second level » analysis • output = raw signal, contrast images and statistical maps

7. PET scan

8. X = + Y General Linear Model N: # images p: # regressors • GLM defined by: • design matrix X • error term ε distribution

9. Design matrix example Single subject fMRI time series Group comparison with two-sample t-test

10. T-test & contrast A contrast selects a specific effect of interest: contrast c = vector of length p. cTβ= linear combination of regression coefficients β. cT = [1 0 0 0 0 …] cTβ = 1xb1 + 0xb2 + 0xb3 + 0xb4 + 0xb5 + . . . cT = [0 -1 1 0 0 …] cTβ = 0xb1+-1xb2 + 1xb3 + 0xb4 + 0xb5 + . . . Under i.i.dassumptions (for error term ε):

11. Statistics: p-values adjusted for search volume set-level cluster-level voxel-level mm mm mm p c p k p p p T Z p ( ) corrected E uncorrected FWE-corr FDR-corr uncorrected º 0.000 10 0.000 520 0.000 0.000 0.000 13.94 Inf 0.000 -63 -27 15 SPMresults: 0.000 0.000 12.04 Inf 0.000 -48 -33 12 0.000 0.000 11.82 Inf 0.000 -66 -21 6 10 Height threshold T = 3.2057 {p<0.001} 0.000 426 0.000 0.000 0.000 13.72 Inf 0.000 57 -21 12 0.000 0.000 12.29 Inf 0.000 63 -12 -3 voxel-level 0.000 0.000 9.89 7.83 0.000 57 -39 6 20 mm mm mm 0.000 35 0.000 0.000 0.000 7.39 6.36 0.000 36 -30 -15 T Z p ( ) 0.000 9 0.000 0.000 0.000 6.84 5.99 0.000 51 0 48 uncorrected º 0.002 3 0.024 0.001 0.000 6.36 5.65 0.000 -63 -54 -3 0.000 8 0.001 0.001 0.000 6.19 5.53 0.000 -30 -33 -18 30 13.94 Inf 0.000 -63 -27 15 0.000 9 0.000 0.003 0.000 5.96 5.36 0.000 36 -27 9 0.005 2 0.058 0.004 0.000 5.84 5.27 0.000 -45 42 9 12.04 Inf 0.000 -48 -33 12 0.015 1 0.166 0.022 0.000 5.44 4.97 0.000 48 27 24 40 11.82 Inf 0.000 -66 -21 6 0.015 1 0.166 0.036 0.000 5.32 4.87 0.000 36 -27 42 13.72 Inf 0.000 57 -21 12 12.29 Inf 0.000 63 -12 -3 50 9.89 7.83 0.000 57 -39 6 7.39 6.36 0.000 36 -30 -15 60 6.84 5.99 0.000 51 0 48 6.36 5.65 0.000 -63 -54 -3 70 6.19 5.53 0.000 -30 -33 -18 5.96 5.36 0.000 36 -27 9 80 5.84 5.27 0.000 -45 42 9 5.44 4.97 0.000 48 27 24 0.5 1 1.5 2 2.5 5.32 4.87 0.000 36 -27 42 1 Design matrix t-test example: Passive wordlistening versus rest cT = [ 1 0 ] Q: activation during listening ? Null hypothesis:

12. Classical inference u • The Null Hypothesis H0 • = what we want to disprove (no effect). • The Alternative Hypothesis HA • = outcome of interest.  Significance level α: Acceptable false positive rate α.  threshold uα Null Distribution of T t Observation of test statistic t = a realisation of T P-val  Reject H0 in favour of HA if t > uα p-value = evidence against H0. Null Distribution of T

13. RSS0 RSS F-test & contrast Null Hypothesis H0: True model is X0 (reduced model) X0 X0 X1 Test statistic: ratio of explained variability and unexplained variability (error) 1 = rank(X) – rank(X0) 2 = N – rank(X) Full model ? or Reduced model?

14. F-test example: movement related effects

15. t > 0.5 t > 3.5 t > 5.5 Multiple comparison problem High Threshold Med. Threshold Low Threshold Good SpecificityPoor Power(risk of false negatives) Poor Specificity(risk of false positives)Good Power

16. Signal Multiple comparison problem Noise Signal+Noise

17. Use of ‘uncorrected’ p-value, a = 0.1 11.3% 11.3% 12.5% 10.8% 11.5% 10.0% 10.7% 11.2% 10.2% 9.5% Percentage of Null Pixels that are False Positives Multiple comparison problem Use of ‘corrected’ p-value, a=0.1 FWE

18. More inference levels

19. Conclusion From a ‘machine learner’ perspectives, GLM is useful for: • Check for « is there any effect? » • Data filtering (i.e. confound removal) • HRF deconvolution for fMRI • Feature selection/masking 19

20. Thank you for your attention! Any question?