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Semi-Supervised State Space Models

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  1. Semi-Supervised State Space Models

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

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

  4. A Running Example

  5. Dyscalculia Dyslexia 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 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 Inter-voxel differences contain information! http://www.mrc-cbu.cam.ac.uk/people/nikolaus.kriegeskorte/infonotacti.html

  14. Brain States

  15. 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 • PertinentQuestion: 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 ? Is Zt1 < Zt2 ,or Zt2 < Zt3 ,or Sort Zt1, Zt2, Zt3 Zt1 Zt2 Zt3

  23. State Space Model

  24. Comprehensive Model

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

  26. Computational Workflow

  27. Feature Space Estimation

  28. Functional Distance

  29. Transportation Distance

  30. Functional Distance Zt – activation patterns f - transportation

  31. Transportation Distance

  32. Functional Connectivity Estimation

  33. Clustering in Functional Space

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

  35. Embeddings

  36. A Solution Distortion minimizing

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

  38. Working in Feature Space Φ

  39. Feature Selection

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

  41. Estimation

  42. Chosen Method

  43. Premise - EM Algorithm

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

  45. Mean Field Approximation

  46. Experimental Conditions

  47. Comprehensive Model

  48. Comparisons

  49. HRFs

  50. Optimal States