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Probabilistic Models of Cognition: Generative models Table of Contents Chapter Content Generative Model Example: Plinko Machine Working Model can be used captures some for simulation structure of the world in useful way

  1. Probabilistic Models of Cognition: Generative models

  2. Table of Contents ● ● ●

  3. Chapter Content

  4. Generative Model

  5. Example: Plinko Machine

  6. Working Model can be used captures some for simulation structure of the world in useful way

  7. Plinko Machine Demo ● Simulate outcomes (data) many times, shape emerges ● Reason about ‘shape of expected outcomes’ (with probabilistic concepts) ● How to formally describe simulations/working models?

  8. Building Generative Models …

  9. Examples with Flip

  10. Flip ● ●

  11. Flip Sum ● ○ ●

  12. Flipping Coins Bend ●

  13. Flipping Coins Bend ● var bend = function(coin) { return function() { (coin() == 'h') ? makeCoin(0.7)() : makeCoin(0.1)() } }

  14. Flipping Coins Bend ● ● ● ●

  15. Flipping Coins Repeat Sum ● ● ● ● ●

  16. Causal Models in Medical Diagnosis ● ● ● ●

  17. Advanced Causal Models in Medical Diagnosis ● ● ●

  18. Probability Concepts and WebPPL

  19. Probability ● ● ●

  20. Probability Distribution ● ● ● ●

  21. Distributions in WebPPL ● ● ● ●

  22. Distributions in WebPPL ● ● ● ●

  23. Constructing marginal distributions: Infer ● ● ● ● ●

  24. Constructing marginal distributions: Infer ● ● ○ ○

  25. ● ●

  26. The Rules of Probability

  27. Product Rule ● ● ● ● ● ○

  28. Product Rule ● ● ● ●

  29. Product Rule ● ● ● ● ●

  30. Product Rule ● ● ● ●

  31. Product Rule ● ○ ∣ ○ ● ∣

  32. Product Rule ● ● ● ● ●

  33. Sum Rule ● ● ● ●

  34. Sum Rule ● ○ ○ ○

  35. Sum Rule ● ● ● ●

  36. Sum Rule and Product Rule ●

  37. Sum Rule and Product Rule ● ●

  38. Sum Rule and Product Rule ● ●

  39. Advanced WebPPL

  40. Stochastic recursion ● ● ●

  41. Persistent Randomness: mem ● ● ● ●

  42. Persistent Randomness: mem ● ● ●

  43. Persistent Randomness: mem ●

  44. Persistent Randomness: mem ● ● ● ● ●

  45. Example: Intuitive physics

  46. Example: Intuitive physics ● ●

  47. Example: Intuitive physics ● ●

  48. Example: Intuitive physics ●

  49. Example: Intuitive physics ● ○ ○ ○ ○

  50. Summary of Chapter Content ● ● ● ● ● ○ ● ○ ● ○

  51. Exercises

  52. Exercise 1 a) ● ● ○ ○ ● ○ ○

  53. Exercise 1 a) ● ● ○ ○ ● ○

  54. Exercise 1 a) ●

  55. Exercise 1 b) ● ● ●

  56. Exercise 1 c) ●

  57. Exercise 1 c) ● ○

  58. Exercise 1 c) ● ○ ○

  59. Exercise 1 c) ● ○ ○ ● ○ ○

  60. Exercise 2 Just one execution of flip

  61. Exercise 2 b) ●

  62. Exercise 2 c) ● ●

  63. Exercise 3

  64. Exercise 3 a) ● ● ● ●

  65. Exercise 3 b) ● ● ● ● ● ● ●

  66. Exercise 4 a) ● ● ●

  67. Exercise 4 b) ●

  68. Exercise 4 c) ● ●

  69. Exercise 4 c) ● ● ●

  70. Exercise 5 ● ● ○

  71. Exercise 5 a) ● ● ○

  72. Exercise 5 a) ● ○

  73. Exercise 6 a) ● ○

  74. Exercise 6 b) ● ○

  75. Exercise 7 a) ● ●

  76. Exercise 7 b) ●

  77. Exercise 8 a) ● ○ ○ ○ ■

  78. Exercise 8 b) ●

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