1. Semi-Supervised State Space Models

2. A Big Thanks To Prof. Jason Bohland Quantitative Neuroscience Laboratory Boston University Istavan (Pisti) Morocz, Harvard, MNI Firdaus Janoos, OSU/Harvard,MIT/Exxon

3. Sources http://neufo.org/lecture_events NIPS 2011

4. A Running Example

5. Difficulty in learning arithmetic that cannot be explained by mental retardation, inappropriate schooling, or poor social environment Core conceptual deficit dealing with numbers Very common : 3-6% of school-age children Heterogeneous DyscalculiaDyslexia Selective inability to build a visual representation of a word, used in subsequent language processing, in the absence of general visual impairment or speech disorders Affects 5-10% of the population Spelling, phonological processing, word retrieval Disorder of the visual word form system Multiple varieties Occipital, temporal, frontal, cerebellum

6. Experimental protocols Event-related designs -single stimuli/“events” at any time point -Periodic or spread across frequencies -Require rapidly acquired data(small TR) -Rapid events (less than ~20s apart) give rise to temporal summation of BOLD response -Summation is close to linear, but non-linearities are evident for small ISIs. Stimulus function (s(t))

7. Mental Arithmetic Paradigm

8. Mental Arithmetic Involves basic manipulation of number and quantities Magnitude based system – bilateral IPS Verbal based system – left AG Attentional system – ps Parietal Lobule Other systems – SMA, primary visual cortex, liPFC, insula, etc

9. Cascadic Recruitment

10. Classical fMRI Pipeline

11. State-of-the-Art - ROI Janoos et al., EuroVis2009

12. Another Way ?

13. Multi-voxel pattern analysis Traditional analyses focus has focused on relationship between task and individual brain voxels (or regions) MVPA uses patterns of observed activation across sets of voxels to decode represented information –Relies on machine learning / pattern classification algorithms –Claim: more sensitive detection of cognitive states (Mind Reading) –Does not employ spatial smoothing –Typically conducted within individual subjects http://www.mrc-cbu.cam.ac.uk/people/nikolaus.kriegeskorte/infonotacti.html Inter-voxel differences contain information!

14. Brain States

16. Inspiration

17. Haxby, 2001

18. Mitchell, 2008

19. Functional Networks

20. Functional / Effective Connectivity Standard analysis of fMRI data conforms to a functional segregation approach to brain function i.e. brain regions are active for a stimulus type Assumes the inputs have access to all brain regions Pertinent Question: How do active brain regions interact with one another? [ functional integration ] Effective Connectivity = the functional strength of a specific anatomical connection during a particular cognitive task; i.e. the influence that one region has on another. ( Inferred ) Functional Connectivity = the temporal correlation between signal from two brain regions during a cognitive task ( Measured ) [ But these are exceptionally fuzzy terms ]

21. A Solution – State Space Models

22. Functional Distance ? Zt 1 Zt 2 Zt 3 Is Zt 1 < Zt 2,or Zt 2 < Zt 3,or Sort Zt 1, Zt 2, Zt 3

23. State Space Model

24. Comprehensive Model

25. State-Space Model Janoos et al., MICCAI 2010

26. Computation al Workflow

27. Feature Space Estimation

28. Functional Distance

29. Transportation Distance

30. Functional Distance Z t – activation patterns f - transportation

31. Transportation Distance

32. Functional Connectivity Estimation

33. Algorithm

34. Clustering in Functional Space

35. Critique No neurophysiologic model Point estimates Hemodynamic uncertainty Temporal structure Functional distance - an optimization problem No metric structure Expensive !

36. Embeddings

37. A Solution Distortion minimizing

38. Feature Space Φ Orthogonal Bases Graph Partitioning Normalized graph Laplacian of F

39. Working in Feature Space Φ

40. Feature Selection

41. Model Size Selection Strike balance between model complexity and model fit Information theoretic or Bayesian criteria Notion of model complexity Cross-validation IID Assumption

42. Estimation

43. Chosen Method

44. Premise - EM Algorithm

45. Generalized EM Algorithm http://mplab.ucsd.edu/tutorials/EM.pdf

46. Mean Field Approximation

47. Experimental Conditions

48. Comprehensive Model

49. Comparisons

50. HRFs

51. Optimal States

52. Spatial Maps

53. Population Studies (sort of)

54. Interpretation Janoos et al., NeuroImage, 2011 Control Dyscalculic Dyslexic

55. MDS Plots

57. Stage-wise Error Plots

58. Phase 1 Phase 2 Phase 1: Product Size Phase 2: Problem Difficulty Stage-wise MDS Plots

59. What Else ?

60. Maximally Predictive Criteria Multiple spatio-temporal patterns in fMRI Neurophysiological task related vs. default networks Extraneous Breathing, pulsatile, scanner drift Select a model that is maximally predictive with respect to task Predictability of optimal state-sequence from stimulus, s

61. “Resting State” Rather than evoked responses, rs-fMRI looks at random, low- frequency fluctuations of BOLD activity (Biswal, 1995)  “industry standard” filters data at ~0.01 < f < 0.08 Hz “Default mode” network (Raichle et al., 2001)  Set of regions with correlated BOLD activity  Activation decreases when subjects perform an explicit task  Ventromedial PFC, precuneus, temporal-parietal junction… But the default mode is only one network that emerges from the correlation structure of resting state networks  Smith et al (2009) showed various task-active networks emerge from ICA based interrogation of rs-fMRI data

62. Summary Process model for fMRI Spatial patterns and the temporal structure Identification of internal mental processes Neurophysiologically plausible Test for the effects of experimental variables Parameter interpretation Comparison of mental processes Abstract representation of patterns

63. Thank You for Putting Up with me for 9 Lectures