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Generative Models

Generative Models. Announcements. Probability Review (Friday, 1:15 Gates B03). Late days…. To be fair…. double late days. Start the p-set early. Where we are. Search. Machine Learning. CS221. Variable Based. Search. Machine Learning. CS221. Variable Based. Search. Machine Learning.

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Generative Models

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  1. Generative Models

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

  3. Where we are

  4. Search Machine Learning CS221 Variable Based

  5. Search Machine Learning CS221 Variable Based

  6. Search Machine Learning CS221 Variable Based

  7. Where We Left Off

  8. Where We Left Off

  9. 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.

  10. 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. Y is all variables that aren’t in X or E These are values in our table! Y is all variables that aren’t in E

  11. 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

  12. Key Idea

  13. Key Idea

  14. Key Idea

  15. Key Idea

  16. Key Idea

  17. Key Idea

  18. Key Idea

  19. Our joint gets too big

  20. Where We Left Off Add variable Snowden location: { Hong Kong, Sao Paulo, Moscow, Nairobi, Caracas, Guantanamo } Size of the table is now 2*2*2*6 = 48 Joint is exponential in size. But what does Snowden have to do with drugged out rockstars? Really are independent…

  21. 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.

  22. What else is independent? Snowden Drugged Purple Loopy

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

  24. What else is independent? Snowden Drugged Purple Loopy Both caused by drugged

  25. What else is independent? Snowden Drugged Purple Loopy If you know drugged, purple and loopy are independent!

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

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

  28. This is important!

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

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

  31. Conditional Independence Drugged Purple Loopy No longer need the full joint.

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

  33. Model the world with variables

  34. And what causes what

  35. Bayesian Network

  36. Bayesian Network

  37. Bayesian Network Stomach Bug Flu Vomit Cough Fever

  38. Bayesian Network Stomach Bug Flu Vomit Cough Fever

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

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

  41. Bayesian Network Joint

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

  43. Formally 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:

  44. What does NSA do with our data?

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

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