Learning to distinguish cognitive subprocesses based on f

Learning to distinguish cognitive subprocesses based on f. MRI 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

Can we distinguish brief cognitive processes using f. MRI? Finds sentence ambiguous or not?

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

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

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

[Anderson, Qin, & Sohn, 2002]

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

Training “Virtual Sensors” of Cognitive Processes Train classifiers of form: f. MRI(t, t+d) Cognitive. Process e. g. , f. MRI(t, t+8) = {Read. Sentence, View. Picture} • Fixed set of cognitive processes • Fixed time interval [t, t+d]

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

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

• Learn f. MRI(t, t+8) {Picture, Sentence}, for t=0, 8 View Picture Or Read Sentence t=0 Fixation 4 sec. picture or sentence? Read Sentence Or View Picture Press Button Rest 8 sec. picture or sentence? Difficulties: only 8 seconds of very noisy data overlapping hemodynamic responses additional cognitive processes occuring simultaneously

Learning task formulation: • Learn f. MRI(t, …, t+8) {Picture, Sentence} – – 40 trials (40 pictures and 40 sentences) f. MRI(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 …

Learning a Gaussian Naïve Bayes (GNB) classifier for <f 1, … fn> C For each class value, ci, 1. Estimate f 1 f 2 … fn 2. For each feature fj estimate 3. fj, as Gaussian, modeling distribution for each ci , Applying GNB classifier to new instance C

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

Support Vector Machines (SVM)

Linear SVM

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’ True error rate Error on training data Variance term related to kernel H complexity and number of training examples m

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

Generative vs. Discriminative Classifiers Discriminative Generative 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

GNB vs. Logistic regression [Ng, Jordan NIPS 03] Gaussian naïve Bayes Logistic regression • Model P(X|C) as a classconditional Gaussian • Model P(C|X) as a logistic function • Decision surface: hyperplane • Learning converges in O(log(n)) examples, where n is number of data attributes • Learning converges in O(n) examples • Asymptotic error less or same as GNB

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

Can We Train Subject-Indep Classifiers?

Training Cross-Subject Classifiers for Picture/Sentence [Wang, Hutchinson, Mitchell. NIPS 03] • Approach 1: 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

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

Learning task formulation • Learn f. MRI(t, …, t+32) Word. Category – f. MRI(t, …t+32) represented by mean f. MRI 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

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%

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

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 1 Subject 2 Subject 3

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

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.

Six-Category Study: Pairwise Classification Errors (ventral temporal cortex) * Worst * Best Subj 1 Sub 2 Sub 3 Sub 4 Sub 5 Sub 6 Sub 7 Mean Fish Vegetables Tools Dwellings Trees Bldg Parts . 20. 10 *. 20. 15. 60 *. 20. 15. 23 . 55 *. 35 *. 45 *. 55. 25. 55 *. 46 . 20. 35. 15 *. 15. 25. 00 *. 15. 18 . 15. 20. 30 *. 25. 21 . 05 *. 30. 20. 05 *. 15 *. 05 *. 12 . 15. 10 *. 20. 25. 15 *. 30 *. 15. 19

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

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

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

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

Which Feature Selection Works Best? Wish to learn F: <x 1, x 2, …xn> {A, B} • Conventional wisdom: pick features xi that best distinguish between classes A and B – E. g. , sort xi by mutual information, choose the top n • Surprise: Alternative strategy worked much better

The learning setting Class A Class B Voxel discriminability Voxel activity Rest / Fixation

GNB Classifier Errors: Feature Selection feature selection method f. MRI study All features Discriminate target classes Active ROI Active Average Picture Syntactic Sentence Ambiguity Nouns vs. Verbs Word Categories . 29. 26 . 43. 34 . 36 . 10 . 16. 18. 21 . 25. 27 . 34. 31. 23 . 08. 09 NA

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

“Zero Signal” learning setting Conjecture: feature selection using discrim(Z, Xi) 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

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

Bayes Net related State-Space Models HMM’s, DBNs, etc. e. g. , [Ghahramani, 2001] Cognitive subprocesses / state variables: f. MRI: see [Hojen-Sorensen et al, NIPS 99]

Hidden Process Model [with Rebecca Hutchinson] Each process defined by: – Process. ID: <comprehend sentence> – Maximum HDR duration: R – Emission. Distribution: [ W(v, t) ] Interpretation Z of data: set of process instances – Desire max likelihood { <Process. IDi, Start. Timei>} – Where data likelihood is Generative model for classifying overlapping hidden processes

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

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

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

OLS learns 2 processes, overlapping in time, 1 voxel, zero noise, start times known, 10 trials [Indra Rustandi] Observed data Learned process 1 Estimates: -0 0. 25 0. 75 1 0. 75 0. 25 3. 5108 e-17 Reconstructed data Learned process 2 -4. 7535 e 17 0. 5 0. 5

OLS learns 2 processes, overlapping in time, 1 voxel, noise 0. 2, start times known, 10 trials [Indra Rustandi] Observed data Reconstructed data Learned process 1 Learned process 2 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

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

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

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

Initial results: HPM’s on Pict. Sent • 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)

Further reading • Carlson, et al. , J. Cog. Neurosci, 2003 • Cox, D. D. and R. L. Savoy, Functional magnetic resonance imaging (f. MRI) ``brain reading'': detecting and classifying distributed patterns of f. MRI activity in human visual cortex. Neuro. Image, 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, Neuro. Image 15, pp. 772 --786, 2002. • Mitchell, T. M. , R. Hutchinson, M. Just, S. R. Niculescu, F. Pereira, X. Wang, Classifying Instantaneous Cognitive States from f. MRI 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. La. Conte, and D. Rottenberg. The quantitative evaluation of functional neuroimaging experiments: The NPAIRS data analysis framework. Neuro. Image 15: 747 -771, 2002. • Wang, X. , R. Hutchinson, and T. ~M. Mitchell. Training f. MRI Classifiers to Detect Cognitive States across Multiple Human Subjects. Proceedings of the 2003 Conference on Neural Information Processing Systems, Vancouver, December 2003.