1. Generative Models

3. Announcements Probability Review (Friday, 1:15 Gates B03) Late days… To be fair… Start the p-set early double late days.

4. Where we are

5. Machine Learning Variable Based Search CS221

6. Machine Learning Variable Based Search CS221

7. Machine Learning Search Variable Based CS221

10. Where We Left Off

11. LoopyNot loopy PurpleNot PurplePurpleNot Purple Drugged0.1080.0120.0720.008 Not Drugged0.0160.0640.1440.576

12. Key Idea If we have a joint distribution over all variables, then given evidence (which could be multiple variables) E = e, we can find the probability of any query variable X = x.

13. These are values in our table! Y is all variables that aren’t in X or E Y is all variables that aren’t in E Key Idea If we have a joint distribution over all variables, then given evidence (which could be multiple variables) E = e, we can find the probability of any query variable X = x.

14. Key Idea If we have a joint distribution over all variables, then given evidence (which could be multiple variables) E = e, we can find the probability of any query variable X = x. Since we know that p(x | e)’s must sum to 1

15. LoopyNot loopy PurpleNot PurplePurpleNot Purple Drugged0.1080.0120.0720.008 Not Drugged0.0160.0640.1440.576 Key Idea

16. LoopyNot loopy PurpleNot PurplePurpleNot Purple Drugged0.1080.0120.0720.008 Not Drugged0.0160.0640.1440.576 Key Idea

17. LoopyNot loopy PurpleNot PurplePurpleNot Purple Drugged0.1080.0120.0720.008 Not Drugged0.0160.0640.1440.576 Key Idea

18. LoopyNot loopy PurpleNot PurplePurpleNot Purple Drugged0.1080.0120.0720.008 Not Drugged0.0160.0640.1440.576 Key Idea

19. LoopyNot loopy PurpleNot PurplePurpleNot Purple Drugged0.1080.0120.0720.008 Not Drugged0.0160.0640.1440.576 Key Idea

20. LoopyNot loopy PurpleNot PurplePurpleNot Purple Drugged0.1080.0120.0720.008 Not Drugged0.0160.0640.1440.576 Key Idea

22. Our joint gets too big

23. Where We Left Off LoopyNot loopy PurpleNot PurplePurpleNot Purple Drugged0.1080.0120.0720.008 Not Drugged0.0160.0640.1440.576 Add variable Snowden location: { Hong Kong, Sao Paulo, Moscow, Nairobi, Caracas, Guantanamo } Size of the table is now 2*2*2*6 = 48 But what does Snowden have to do with drugged out rockstars? Really are independent… Joint is exponential in size.

24. Independence l = loopy p = purple d = drugged s = snowden If we have two tables, one over l, p, d and one for s, we could recreate the joint.

25. What else is independent? Snowden Drugged Purple Loopy

26. What else is independent? Snowden Drugged Purple Loopy Purple and loopy?

27. What else is independent? Snowden Drugged PurpleLoopy Both caused by drugged

28. What else is independent? Snowden Drugged PurpleLoopy If you know drugged, purple and loopy are independent!

29. Conditional Independence If you know drugged, purple and loopy are independent!

30. Conditional Independence Joint

31. This is important!

32. If you know drugged, purple and loopy are independent! Conditional Independence Joint

33. If you know drugged, purple and loopy are independent! Conditional Independence Joint

34. Drugged PurpleLoopy No longer need the full joint. Conditional Independence

35. We only need p(var | causes) for each var.

36. Model the world with variables

37. And what causes what

38. Bayesian Network

40. Cough Fever Vomit Flu Stomach Bug

41. Bayesian Network Cough Fever Vomit Flu Stomach Bug

42. Bayesian Network Cough (c) Fever (t) Vomit (v) Flu (f) Stomach bug (s)

43. Bayesian Network Cough (c) Vomit (v) Flu (f) Stomach bug (s) Joint Fever (t)

44. Bayesian Network Joint

45. Bayesian Network Cough (c) Fever (t) Vomit (v) Flu (f) Stomach bug (s) Joint

46. Definition: Bayes Net = DAG DAG: directed acyclic graph (BN’s structure) Nodes: random variables (typically discrete, but methods also exist to handle continuous variables) Arcs: indicate probabilistic dependencies between nodes. Go from cause to effect. CPDs: conditional probability distribution (BN’s parameters) Conditional probabilities at each node, usually stored as a table (conditional probability table, or CPT) Root nodes are a special case – no parents, so just use priors in CPD: Formally

48. What does NSA do with our data?

49. Real World Problem Formal Problem Solution Model the problem Apply an Algorithm Evaluate The AI Pipeline

51. Live Research

52. Research Project g3g3 t1t1 t2t2 t3t3 e1e1 e2e2 e3e3 g1g1 g2g2 b i ?

53. g3g3 t1t1 t2t2 t3t3 e1e1 e2e2 e3e3 g1g1 g2g2 b i ?

54. g1g1 g1*g1* ?

55. Modeling Surprise g1g1 g1*g1* ?

56. Competition Chose top 5 Test how well they predict grades Select a finalist (gets +) TA Review Actually re-grade Publish?

57. On worst pset question Prize + Due Tuesday before class (email staff. Subject: Modeling Regrades)

58. Novel Science

59. http://vimeo.com/60381274

60. What does NSA do with our data?

62. Research Project g3g3 t1t1 t2t2 t3t3 e1e1 e2e2 e3e3 g1g1 g2g2 b i ?

63. Can someone fix this?

64. Peer Graders