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Part II: Practical Implementations. PowerPoint Presentation
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Part II: Practical Implementations.

Part II: Practical Implementations.

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Part II: Practical Implementations.

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  1. Part II: Practical Implementations.

  2. Modeling the Classes Stochastic Discrimination

  3. Algorithm for Training a SD Classifier Generate projectable weak model Evaluate model w.r.t. training set, check enrichment Check uniformity w.r.t. existing collection Add to discriminant

  4. Dealing with Data Geometry:SD in Practice

  5. 2D Example • Adapted from [Kleinberg, PAMI, May 2000]

  6. An “r=1/2” random subset in the feature space that covers ½ of all the points

  7. Watch how many such subsets cover a particular point, say, (2,17) (2,17)

  8. Out In In It’s in 1/2 models Y = ½ = 0.5 It’s in 2/3 models Y = 2/3 = 0.67 It’s in 0/1 models Y = 0/1 = 0.0 In In In It’s in 3/4 models Y = ¾ = 0.75 It’s in 4/5 models Y = 4/5 = 0.8 It’s in 5/6 models Y = 5/6 = 0.83

  9. Out In In It’s in 6/8 models Y = 6/8 = 0.75 It’s in 7/9 models Y = 7/9 = 0.77 It’s in 5/7 models Y = 5/7 = 0.72 In Out Out It’s in 8/10 models Y = 8/10 = 0.8 It’s in 8/11 models Y = 8/11 = 0.73 It’s in 8/12 models Y = 8/12 = 0.67

  10. Fraction of “r=1/2” random subsets covering point (2,17) as more such subsets are generated

  11. Fractions of “r=1/2” random subsets covering several selected points as more such subsets are generated

  12. Distribution of model coverage for all points in space, with 100 models

  13. Distribution of model coverage for all points in space, with 200 models

  14. Distribution of model coverage for all points in space, with 300 models

  15. Distribution of model coverage for all points in space, with 400 models

  16. Distribution of model coverage for all points in space, with 500 models

  17. Distribution of model coverage for all points in space, with 1000 models

  18. Distribution of model coverage for all points in space, with 2000 models

  19. Distribution of model coverage for all points in space, with 5000 models

  20. Introducing enrichment: For any discrimination to happen, the models must have some difference in coverage for different classes.

  21. Class distribution A biased (enriched) weak model • Enforcing enrichment (adding in a bias): require each subset to cover more points of one class than another

  22. Distribution of model coverage for points in each class, with 100 enriched weak models

  23. Distribution of model coverage for points in each class, with 200 enriched weak models

  24. Distribution of model coverage for points in each class, with 300 enriched weak models

  25. Distribution of model coverage for points in each class, with 400 enriched weak models

  26. Distribution of model coverage for points in each class, with 500 enriched weak models

  27. Distribution of model coverage for points in each class, with 1000 enriched weak models

  28. Distribution of model coverage for points in each class, with 2000 enriched weak models

  29. Distribution of model coverage for points in each class, with 5000 enriched weak models

  30. Error rate decreases as number of models increases Decision rule: if Y < 0.5 then class 2 else class 1

  31. Training Set Test Set • Sparse Training Data: Incomplete knowledge about class distributions

  32. Distribution of model coverage for points in each class, with 100 enriched weak models Training Set Test Set

  33. Distribution of model coverage for points in each class, with 200 enriched weak models Training Set Test Set

  34. Distribution of model coverage for points in each class, with 300 enriched weak models Training Set Test Set

  35. Distribution of model coverage for points in each class, with 400 enriched weak models Training Set Test Set

  36. Distribution of model coverage for points in each class, with 500 enriched weak models Training Set Test Set

  37. Distribution of model coverage for points in each class, with 1000 enriched weak models Training Set Test Set

  38. Distribution of model coverage for points in each class, with 2000 enriched weak models Training Set Test Set

  39. No discrimination! • Distribution of model coverage for points in each class, with 5000 enriched weak models Training Set Test Set

  40. Models of this type, when enriched for training set, are not necessarily enriched for test set Training Set Test Set Random model with 50% coverage of space

  41. Introducing projectability: Maintain local continuity of class interpretations. Neighboring points of the same class should share similar model coverage.

  42. Class distribution A projectable model • Allow some local continuity in model membership, so that interpretation of a training point can generalize to its immediate neighborhood

  43. Distribution of model coverage for points in each class, with 100 enriched, projectable weak models Training Set Test Set

  44. Distribution of model coverage for points in each class, with 300 enriched, projectable weak models Training Set Test Set

  45. Distribution of model coverage for points in each class, with 400 enriched, projectable weak models Training Set Test Set

  46. Distribution of model coverage for points in each class, with 500 enriched, projectable weak models Training Set Test Set

  47. Distribution of model coverage for points in each class, with 1000 enriched, projectable weak models Training Set Test Set

  48. Distribution of model coverage for points in each class, with 2000 enriched, projectable weak models Training Set Test Set

  49. Distribution of model coverage for points in each class, with 5000 enriched, projectable weak models Training Set Test Set

  50. Promoting uniformity: All points in the same class should have equal likelihood to be covered by a model of each particular rating. Retain models that cover the points whose coverage by current collection is less