1. Learning to distinguish cognitive subprocesses based on fMRI Tom M. Mitchell Center for Automated Learning and Discovery Carnegie Mellon University Collaborators: Luis Barrios, Rebecca Hutchinson, Marcel Just, Francisco Pereira, Jay Pujara, John Ramish, Indra Rustandi

2. Can we distinguish brief cognitive processes using fMRI? Finds sentence ambiguous or not?

3. Decide whether consistent Can we classify/track multiple overlapping processes? Observed fMRI: Observed button press: Read sentence View picture

4. Mental Algebra Task [Anderson, Qin, & Sohn, 2002] 24 3 c

5. [Anderson, Qin, & Sohn, 2002] Activity Predicted by ACT-R Model Typical ACT-R rule: IF “_ op a = b” THEN “ _ = a>”

6. [Anderson, Qin, & Sohn, 2002]

7. Outline Training classifiers for short cognitive processes –Examples –Classifier learning algorithms –Feature selection –Training across multiple subjects Simultaneously classifying multiple overlapping processes –Linear Model and classification –Hidden Processes and EM

8. Training “Virtual Sensors” of Cognitive Processes Train classifiers of form: fMRI(t, t+  )  CognitiveProcess e.g., fMRI(t, t+  ) = {ReadSentence, ViewPicture} Fixed set of cognitive processes Fixed time interval [t, t+  ]

9. Study 1: Pictures and Sentences Subject answers whether sentence describes picture by pressing button. 13 subjects, TR=500msec View Picture Or Read Sentence Or View Picture Fixation Press Button 4 sec.8 sec.t=0 Rest Data from [Keller et al., 2001]

10. It is not true that the star is above the plus.

12. + --- *

13. .

14. Learn fMRI(t,t+8)  {Picture,Sentence}, for t=0,8 View Picture Or Read Sentence Or View Picture Fixation Press Button4 sec.8 sec.t=0 Rest picture or sentence? Difficulties: only 8 seconds of very noisy data overlapping hemodynamic responses additional cognitive processes occuring simultaneously

15. Learning task formulation: Learn fMRI(t, …, t+8)  {Picture, Sentence} –40 trials (40 pictures and 40 sentences) –fMRI(t,…t+8) = voxels x time (~ 32,000 features) –Train separate classifier for each of 13 subjects –Evaluate cross-validated prediction accuracy Learning algorithms: –Gaussian Naïve Bayes –Linear Support Vector Machine (SVM) –k-Nearest Neighbor –Artificial Neural Networks Feature selection/abstraction –Select subset of voxels (by signal, by anatomy) –Select subinterval of time –Summarize by averaging voxel activities over space, time –…

16. [Strother et al., 2002]

17. Learning a Gaussian Naïve Bayes (GNB) classifier for  C For each class value, c i, 1.Estimate 2.For each feature f j estimate modeling distribution for each c i, f j, as Gaussian, Applying GNB classifier to new instance f2f2 f1f1 C fnfn …

18. Support Vector Machines [Vapnik et al. 1992] Method for learning classifiers corresponding to linear decision surface in high dimensional spaces Chooses maximum margin decision surface Useful in many high-dimensional domains –Text classification –Character recognition –Microarray analysis

19. Support Vector Machines (SVM)

20. Linear SVM

22. Accepting noise in SVM’s

23. Non-linear Support Vector Machines Based on applying kernel functions to data points –Equivalent to projecting data into higher dimensional space, then finding linear decision surface –Select kernel complexity (H) to minimize ‘structural risk’ Error on training data Variance term related to kernel H complexity and number of training examples m True error rate

24. Generative vs. Discriminative Classifiers Goal: learn, equivalently Discriminative classifier: Learn directly Generative classifier: Learn Classify using

25. Generative vs. Discriminative Classifiers DiscriminativeGenerative What they estimate: P(C|data)P(data|C) Examples: SVM’s, Artificial Neural Nets Naïve Bayes, Bayesian networks Robustness to modeling errors Typically more robust Less robust Criterion for estimating parameters Minimize classification error Maximize data likelihood

26. GNB vs. Logistic regression [Ng, Jordan NIPS03] Gaussian naïve Bayes Model P(X|C) as a class- conditional Gaussian Decision surface: hyperplane Learning converges in O(log(n)) examples, where n is number of data attributes Logistic regression Model P(C|X) as a logistic function Decision surface: hyperplane Learning converges in O(n) examples Asymptotic error less or same as GNB

27. Accuracy of Trained Pict/Sent Classifier Results (leave one out cross validation) –Guessing  50% accuracy –SVM: 91% mean accuracy Single subject accuracies ranged from 75% to 98% –GNB: 84% mean accuracy –Feature selection step important for both ~10,000 voxels x 16 time samples = 160,000 features Selected only 240 voxels x 16 time samples

28. Can We Train Subject-Indep Classifiers?

29. Training Cross-Subject Classifiers for Picture/Sentence Approach1: define “supervoxels” based on anatomically defined brain regions –Abstract to seven brain region supervoxels –Each supervoxel 100’s to 1000’s of voxels Train on n-1 subjects, test on nth subject Result: 75% prediction accuracy over subjects outside training set –Compared to 91% avg. single-subject accuracies –Significantly better than 50% guessing accuracy [Wang, Hutchinson, Mitchell. NIPS03]

30. Study 2: Semantic Word Categories Word categories: Fish Trees Vegetables Tools Dwellings Building parts [Francisco Pereira] Experimental setup: Block design Two blocks per category Each block begins by presenting category name, then 20 words Subject indicates whether word fits category

31. Learning task formulation Learn fMRI(t, …, t+32)  WordCategory –fMRI(t,…t+32) represented by mean fMRI image –Train on presentation 1, test on presentation 2 (and vice versa) Learning algorithm: –1-Nearest Neighbor, based on spatial correlation [after Haxby] Feature selection/abstraction –Select most ‘object selective’ voxels, based on multiple regression on boxcars convolved with gamma function –300 voxels in ventral temporal cortex produced greatest accuracy

32. Results predicting word semantic category Mean pairwise prediction accuracy averaged over 8 subjects: Ventral temporal: 77% (low: 57%, high 88%) Parietal: 70% Frontal: 67% Random guess: 50%

33. Mean Activation per Voxel for Word Categories Tools Dwellings Vegetables one horizontal slice, ventral temporal cortex [Pereira, et al 2004] P(fMRI | WordCategory)

34. Plot of single-voxel classification accuracies. Gaussian naïve Bayes classifier (yellow and red are most predictive). Images from three different subjects show similar regions with highly informative voxels. Subject 1Subject 2Subject 3

35. Single-voxel GNB classification error vs. p value from T-statistic N=10^6, P < 0.0001, Error = 0.51 N=10^3, P < 0.0001, Error = 0.01 Cross validated prediction error is unbiased estimate of the Bayes optimal error – the area under the intersection

36. Question: Do different people’s brains ‘encode’ semantic categories using the same spatial patterns? No. But, there are cross-subject regularities in “distances” between categories, as measured by classifier error rates.

37. Six-Category Study: Pairwise Classification Errors (ventral temporal cortex) FishVegetablesToolsDwellingsTreesBldg Parts Subj1.20.55 *.20.15.05 * Sub2.10 *.55 *.35.20.10 *.30 Sub3.20.35 *.15 *.20 Sub4.15.45 *.15.25.05 * Sub5.60 *.55.25.20.15 * Sub6.20.25.00 *.30 *.05 Sub7.15.55 *.15.25.15.05 * Mean.23.46.18.21.19.12 * Worst * Best

38. LDA classification of semantic categories of photographs. [Carlson, et al., J. Cog. Neurosci, 2003]

39. Cox & Savoy, Neuroimage 2003 Trained SVM and LDA classifiers for semantic photo categories. Classifiers applied to same subject a week later were equally accurate

40. Lessons Learned Yes, one can train machine learning classifiers to distinguish a variety of cognitive processes –Comprehend Picture vs. Sentence –Read ambiguous sentence vs. unambiguous –Read Noun vs. Verb –Read Nouns about “tools” vs. “building parts” Failures too: –True vs. false sentences –Negative vs. affirmative sentences

41. Which Machine Learning Method Works Best? GNB and SVM tend to outperform KNN Feature selection important No Yes Average per-subject classification error

42. Which Feature Selection Works Best? Conventional wisdom: pick features x i that best distinguish between classes A and B –E.g., sort x i by mutual information, choose the top n Surprise: Alternative strategy worked much better Wish to learn F:  {A,B}

43. The learning setting Class AClass B Rest / Fixation Voxel discriminability Voxel activity

44. GNB Classifier Errors: Feature Selection NA.23.27.21 ROI Active Average.09.31.27.18 ROI Active.08.34.25.16 Active.10.36.34.26 Discriminate target classes.10.36.43.29 All features Word Categories Nouns vs. Verbs Syntactic Ambiguity Picture Sentence fMRI study feature selection method

46. X 1 =S 1 +N 1 X 2 =S 2 +N 2 Z = N 0 Goal: learn f: X  Y or P(Y|X) Given: 1.Training examples where X i = S i + N i, signal S i ~ P(S|Y= Y i ), noise N i ~ P noise 2.Observed noise with zero signal N 0 ~ P noise “Zero Signal” learning setting. Zero signal (fixation) Class 1 observations Class 2 observations Select features based on discrim(X 1,X 2 ) or discrim(Z,X i )?

47. “Zero Signal” learning setting Conjecture: feature selection using discrim(Z,X i ) will improve relative to discrim(X 1,X 2 ) as: # of features increases # of training examples decreases signal/noise ratio decreases fraction of relevant features decreases

48. Decide whether consistent 2. Can we classify/track multiple overlapping processes? Observed fMRI: Observed button press: Read sentence View picture Input stimuli: ?

49. Bayes Net related State-Space Models HMM’s, DBNs, etc. e.g., [Ghahramani, 2001] Cognitive subprocesses / state variables: fMRI: see [Hojen-Sorensen et al, NIPS99]

50. Hidden Process Model Each process defined by: –ProcessID: –Maximum HDR duration: R –EmissionDistribution: [ W(v,t) ] Interpretation Z of data: set of process instances –Desire max likelihood { } –Where data likelihood is Generative model for classifying overlapping hidden processes [with Rebecca Hutchinson]

51. Classifying Processes with HPMs Start time known: Start time unknown: consider candidate times S

52. GNB classifier is a special case of HPM classifier View Picture Or Read Sentence Or View Picture Fixation Press Button 4 sec.8 sec.t=0 Rest picture or sentence? 16 sec. GNB: picture or sentence? HPM:

53. Learning HPMs Known start times: Least squares regression, eg. see Dale[HMB, 1999] Unknown start times: EM algorithm –Repeat: Estimate P(S|Y,W) W’  arg max Currently implement M step with gradient ascent

54. OLS learns 2 processes, overlapping in time, 1 voxel, zero noise, start times known, 10 trials Estimates: -0 0.25 0.5 0.75 1 0.75 0.5 0.25 3.5108e- 17 -4.7535e- 17 0.5 [Indra Rustandi] Observed data Reconstructed data Learned process 1 Learned process 2

55. OLS learns 2 processes, overlapping in time, 1 voxel, noise 0.2, start times known, 10 trials Estimates: 0.005495 6 0.32446 0.48847 0.83317 0.99872 0.86555 0.55624 0.23633 - 0.050592 - 0.017376 0.36435 0.36134 0.4856 0.60143 0.46168 0.54137 0.47466 0.52419 [Indra Rustandi] Observed data Reconstructed data Learned process 1 Learned process 2

56. Phase II, Words every 3 seconds. Mean LFEF, subj 08179 Estimate Noun and Verb impulse responses Verb impulse response estimated from above Verb impulse response “ground truth” from non- overlapping stimuli [Indra Rustandi]

57. Decide whether consistent Can we classify/track multiple overlapping processes? Observed fMRI: Observed button press: Read sentence View picture

58. Learned HPM with 3 processes (S,P,D), and R=13sec (TR=500msec). P P SS D? Learned models S P D observed reconstructed D start time picked to be trailStart+18 P P SS D D D?

59. Initial results: HPM’s on PictSent EM chooses start time = 18 for hidden D process Classification accuracy for heldout PS/SP trials = 15/20 = 0.75 Heldout classification accuracy same for 2 process (P,S) and 3 process (P,S,D) models Data likelihood over heldout data slightly better for 3 process (P,S,D)

60. Further reading Carlson, et al., J. Cog. Neurosci, 2003 Cox, D.D. and R.L. Savoy, Functional magnetic resonance imaging (fMRI) ``brain reading'': detecting and classifying distributed patterns of fMRI activity in human visual cortex. NeuroImage, Volume 19, Pages 261--270, 2003. Kjems, U., L. Hansen, J. Anderson, S. Frutiger, S. Muley, J. Sidtis, D. Rottenberg, and S. C. Strother. The quantitative evalutation of functional neuroimaging experiments: mutual information learning curves, NeuroImage 15, pp. 772--786, 2002. Mitchell, T.M., R. Hutchinson, M. Just, S. R. Niculescu, F. Pereira, X. Wang, Classifying Instantaneous Cognitive States from fMRI Data. Proceedings of the 2003 Americal Medical Informatics Association Annual Symposium, Washington D.C., November 2003. Mitchell, T.M., R. Hutchinson, S. R. Niculescu, F. Pereira, X. Wang,, M. Just, S. Newman. Learning to Decode Cognitive States from Brain Images, Machine Learning, 2004. Strother S.C., J. Anderson, L.Hansen, U.Kjems, R.Kustra, J. Siditis, S. Frutiger, S. Muley, S. LaConte, and D. Rottenberg. The quantitative evaluation of functional neuroimaging experiments: The NPAIRS data analysis framework. NeuroImage 15:747-771, 2002. Wang, X., R. Hutchinson, and T.~M. Mitchell. Training fMRI Classifiers to Detect Cognitive States across Multiple Human Subjects. Proceedings of the 2003 Conference on Neural Information Processing Systems, Vancouver, December 2003.