1. Discriminative Network Models of Schizophrenia
G. A. Cecchi
I. Rish
Computational Biology
IBM Watson Research, NY
J.-L. Martinot
M.-L. Paillere-Martinot
M. Plaze
Frédéric Joliot Hospital, CEA
Orsay, France
J.-B. Poline
B. Thyreau
B. Thirion  
Neurospin, CEA
Saclay, France
C. Martelli
Centre Hospitalier P. Brousse
Villejuif, France

2. Affects 0.5-1% of world population Positive symptoms (psychosis):
What schizophrenia is
Affects 0.5-1% of world population
Positive symptoms (psychosis):
Hallucinations
Mostly auditory (theory of “inner speech”)
Delusions
Cognitive – organizational:
Disorganized thoughts
Negative symptoms:
Poor socialization
Not a simple psychiatric disease, not easy to diagnose
As with many things, Europeans and Yanks don’t agree (Bentall, 2003)

3. Schizophrenia as a network disorder
Not a localized dysfunction, spatially or even mechanistically (i.e. dopamine theory)
Schizophrenia is hypothesized to be a disconnection syndrome (Wernicke 1906; Bleuler, 1911; Friston & Frith, 1995)

4. Our Questions
What specific effects does schizophrenia have on functional networks as defined by fMRI?
Are network disruptions explainable by area-specific, task-dependent linear disruptions?
Is it possible to use functional networks to provide for consistent predictive modeling?

5. Patient Group (11 subjects)
Experimental paradigm: simple auditory task*
8,95 secs
4 s
Response 1
Response 2
Tone: 200ms
Silence 750ms
Cue 500 ms
Sentence 3,5 s
Sentence
3,5 s
96 trials, with 32 sentences in French (native), 32 sentences in foreign languages, and 32 silence interval controls. Two runs
Patient Group (11 subjects)
Prone to auditory hallucinations
Native French speakers, right-handed, 3+ yrs. illness
Normal Group (11 subjects)
*M. Plaze, et al., Schizophrenia Research (2006)

6. Our analysis approach
Hypothesis-testing: significant group differences?
Model-driven linear activations (GLM analysis) (no)
Model-driven Region-of-Interest (ROI) analysis (no)
Data-driven functional network topology analysis (yes)
Predictive Modeling: is accurate classification possible? (yes)
Feature Extraction: topological, data-driven vs. linear, model-driven

7. Linear activations: mass-univariate approach
For each voxel, compute a score (e.g., correlation) reflecting how well its activity matches the stimulus sequence
Threshold the scores to select only statistically significant ones
No statistically significant differences across groups
Voxel interactions are ignored?
fMRI activation image and time-course - Courtesy of Steve Smith, FMRIB

8. No statistically significant differences across groups
Model-driven networks: ROI analysis
A priori identified
10 relevant ROI’s
600 ROI’s found through contrast similarity and spatial proximity*
Correlation matrix
No statistically significant differences across groups
‘Wrong’ networks?
*B. Thirion, et al., Human Brain Mapping (2006)

9. Group differences significant
Functional networks: voxel-based correlations *
Network link (i,j)  correlation between BOLD(i) and BOLD(j) is above a threshold (0.7) for all voxels
Degree maps:
degree(voxel i) = number of its neighbors in the network
Variety of degree maps:
Full degree maps
Long-distance degree maps – non-local connections (> 5 voxels apart)
inter-hemispheric degree maps – only links between the hemispheres
Group differences significant
*V. Eguíluz, et al., Physical Review Letters (2005)

10. FDR-corrected (full) Degree Maps
Degree maps reveal a distinctive pattern
- Degree maps show a clear pattern even after FDR correction
- Schizophrenic patients lack “hubs” in auditory/language areas
- Linear activation contrasts not significant, in particular in the hub areas
FDR-corrected (full) Degree Maps
2-sample t-test performed for each voxel in degree and activation maps, followed by FDR correction
Red/yellow: Normal subjects have higher values than Schizophrenics
False-Discovery Rate (FDR):
- degree maps: 1033 voxels
activation maps: 0-7 voxels

11. Moreover: disrupted inter-hemispheric connectivity
normal
schizophrenic
normal
schizophrenic
For each subject, we compute the fraction of inter-hemispheric connections over the total number of connections (relative link density), and plot anormalized histogram over all subjects in a group.
Schizophrenics have significantly less inter-hemispheric links
However, there is no difference in the total number of links
It seems the “disconnection” is a “re-wiring”

12. Classification: degree is a better feature
Degree features consistently outperform activation features
SVM achieves 84% accuracy with full degree maps
Sparse MRF classifier achieves 86% with only voxels!
Support Vector Machines
Sparse Markov Random Fields

13. Degree features are more stable than activations
When selecting top-K most significant voxels over data subsets in leave-subject-out cross-validation, degree maps yield higher overlap (~70% common voxels), unlike activation maps

14. Sparse (Gaussian) Markov Random Field Classifier
L1-regularized inverse-covariance selection problem
Learn an MRF for each class separately
Outperforms linear classifiers (e.g., SVM, Gaussian NB)

15. Thanks for your attention
Conclusions
We present evidence that schizophrenia implies a significant disruption of functional networks, such that
It cannot be explained by a disruption to area-based, linear task-dependent responses, i.e. it affects emergent properties
It is non-local in nature
It can be leveraged to build accurate and stable predictive models, even for a simple task
Thanks for your attention
POSTER T68

17. Beyond Correlations: Learning Probabilistic Graphical Models
Our Focus: Markov Networks
1. Unlike functional (correlation) networks, Markov Networks are probabilistic models allowing for statistical inference:
- predicting future brain states from the past
- classifying current brain states
- assessing the likelihood of the mental disease at early stages, etc.
2. Unlike some other ‘black-box’ predictors, Markov Networks are interpretable:
- edges represent (conditional) dependencies among nodes (genes, voxels)

18. Markov Net Classifiers Make Quite Accurate Predictions
Schizophrenia (Neurospin): Mental state prediction (sentence vs picture):
86% accuracy % accuracy
T. Mitchell et al., Learning to Decode Cognitive States from Brain Images Machine Learning,
MRF classifiers can often exploit informative interactions among variables and outperform state-of-art linear classifiers (e.g., SVM)

19. Markov Networks (Markov Random Fields)

21. References
1. Cecchi, G., Rish, I., R. Garg, Martinot, J-L.,Plaze, M., Thyreau, B., Thirion, B., Poline, J-B. (2009). Predictive Network Models of Schizophrenia. Under review.
2. Scheinberg, K. and Rish, I. (2009) SINCO - a greedy coordinate ascent method for sparse inverse covariance selection problem. Under review.
3. K. Scheinberg, N. Bani Asadi, I. Rish (2009). Sparse MRF Learning with Priors on Regularization Parameters, IBM Technical Report RC24812.
4. N. Bani Asadi, I. Rish, K. Scheinberg, D. Kanevsky, B. Ramabhadran (2009). A MAP Approach to Learning Sparse Gaussian Markov Networks, ICASSP-09.
5. Rish, I., Carroll, M., Cecchi, G. Garg, R., Rao, R., Bani Asadi, N., Scheinberg, K. (2009).
Sparse Modeling in fMRI Analysis. Abstract presented at Human Brain Mapping (HBM 2009).
6. Carroll, M. K., Cecchi, G., Rish, I., Garg, R., Rao, A. R. (2009) Prediction and Interpretation of Distributed Neural Activity with Sparse Models, Neuroimage, Jan
7. M. Plaze et al. (2006). Left superior temporal gyrus activation during sentence perception negatively correlates with auditory hallucination severity in schizophrenia patients. Schizophrenia Research, Volume 87, Issue 1, Pages
8. V.M. Eguiluz D.R. Chialvo, G.A. Cecchi, M. Baliki, A.V. Apkarian (2005). Scale-free functional brain networks. Phys. Rev. Letters 94,
9. Y. Liu et al. (2008). Disrupted small-world networks in schizophrenia. Brain, Feb

22. Classification: degree vs. activation features