1. Variables “To be is to be the value of a variable.” - William Quine

2. Announcements Pset 1 and prog 1 were due yesterday Pset 2 and prog 2 are going out today Tiny (intro) email backlog Probability Review is… TBA still Mistake on Alpha / Beta agent algorithm

3. def miniMax(self, node, depth, alpha, beta, isMax): if node.isTerminal(): if isMax return node.utility() return –node.utility() if depth == 0: return self.getHeuristic(node) if isMax: for action in node.getLegalActions(): child = node.getSuccessorState(action) value = miniMax(child, depth -1, alpha, beta, not isMax) alpha = max(alpha, value) if beta <= alpha: break return alpha else: for action in node.getLegalActions(): child = node.getSuccessorState(action) value = self.miniMax(child, depth -1, alpha, beta, not isMax) beta = min(value, beta) if beta <= alpha: break return beta Alpha Beta Pruning return node.utility()

4. Programming Assignment Time

5. Consider asking for help. Email your TA (or rock on)

6. Problem Set Question Time

7. Total: 28 Hours / Student Ideal: 26 Hours / Student Units: 4.2 unit class

8. Homework Preference

9. Driverless Car Important Algo. Easy to Visualize Less Time Driverless Car

10. Search Variable Based Machine Learning CS221

11. Search Variable Based Machine Learning CS221

18. Image Segmentation

19. Chris Claire Home

20. Image Segmentation

22. Motivating Example

24. CSPs Commutatively: the order of application of actions has no effect on outcome

25. CSPs

26. Interesting in their own right Introduction to variable based models Inference is very similar to … [super secret stuff]

27. Formalization Inference Search Improved Search Arc Consistency Graph Structure Genetic Algorithms Weighted CSPs Image Segmentation CSPs

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

29. Formally

30. Factor Graphs

31. Types of Domains

32. Constraints

33. Variables WA, NT, Q, NSW, V, SA, T Domains D i = {red,green,blue} Constraints: adjacent regions must have different colors e.g., WA ≠ NT, or (WA,NT) in {(red,green),(red,blue),(green,red), (green,blue),(blue,red),(blue,green)} Example: Map Coloring

34. 4 Feb 2004CS 3243 - Constraint Satisfaction34 Variables: F T U W R O X 1 X 2 X 3 Domains: {0,1,2,3,4,5,6,7,8,9} Constraints: – Alldiff (F,T,U,W,R,O) – O + O = R + 10 · X 1 – X 1 + W + W = U + 10 · X 2 – X 2 + T + T = O + 10 · X 3 – X 3 = F, T ≠ 0, F ≠ 0 Example: Crypto

35. Example: Student Seats Go!

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

37. Inference 1. Search 2. Constraint Propagation

38. Variables WA, NT, Q, NSW, V, SA, T Domains D i = {red,green,blue} Constraints: adjacent regions must have different colors e.g., WA ≠ NT, or (WA,NT) in {(red,green),(red,blue),(green,red), (green,blue),(blue,red),(blue,green)} Example 2: Map Coloring

39. Solutions are complete and consistent assignments, e.g., WA = red, NT = green,Q = red,NSW = green,V = red,SA = blue,T = green Example 2: Map Coloring

40. Binary CSP: each constraint relates two variables Constraint graph: nodes are variables, arcs are constraints Example 2: Map Coloring

41. Inference 1. Search 2. Constraint Propagation

42. 4 Feb 2004CS 3243 - Constraint Satisfaction42 Search

46. General-purpose methods can give huge gains in speed: Which variable should be assigned next? In what order should its values be tried? Can we detect inevitable failure early? Improved Search

47. Choose the variable with the fewest legal values a.k.a. minimum remaining values (MRV) heuristic Most Constrained Variable

48. Tie-breaker among most constrained variables Choose the variable with the most constraints on remaining variables Most Constraining Variable

49. Given a variable, choose the assignment that rules out the fewest values in the remaining variables Least Constraining Assignment Fun fact: Combining these heuristics makes 1000 queens feasible

50. Inference 1. Search 2. Constraint Propagation

51. 4 Feb 2004CS 3243 - Constraint Satisfaction51 Idea: Keep track of remaining legal values for unassigned variables Terminate search when any variable has no legal values Forward Checking

52. 4 Feb 2004CS 3243 - Constraint Satisfaction52 Idea: Keep track of remaining legal values for unassigned variables Terminate search when any variable has no legal values Forward Checking

53. 4 Feb 2004CS 3243 - Constraint Satisfaction53 Idea: Keep track of remaining legal values for unassigned variables Terminate search when any variable has no legal values Forward Checking

54. 4 Feb 2004CS 3243 - Constraint Satisfaction54 Idea: Keep track of remaining legal values for unassigned variables Terminate search when any variable has no legal values Forward Checking Other ways to catch other failures

55. 4 Feb 2004CS 3243 - Constraint Satisfaction55 At each iteration, make each arc consistent Arc Consistency

56. 4 Feb 2004CS 3243 - Constraint Satisfaction56 At each iteration, make each arc consistent Arc Consistency

57. 4 Feb 2004CS 3243 - Constraint Satisfaction57 At each iteration, make each arc consistent Arc Consistency

58. 4 Feb 2004CS 3243 - Constraint Satisfaction58 At each iteration, make each arc consistent Arc Consistency

59. Graph Structure

60. Theorem: If a constraint graph has no loops then the CSP can be solved in O(nd 2 ) time linear in the number of variables! Compare difference with general CSP, where worst case is O(d n ) Trees are Easy

61. Non Trees

62. Tree Decomposition

63. Motivating Example Sudoku becomes easy (under 0.1s)

64. Flavors

65. Weighted CSP A B weight

66. Demo Example

68. Image Segmentation?

70. Genetic Algorithms Variables D = (D 1, D 2 … D n ) each with domain = {A, T, G, C} Try searching by creating populations, mating them with one another and mutating every once in a while. Just for fun!

71. Genetic Algorithms Just for fun!

72. Genetic Algorithms Just for fun!

73. Theme?

77. Mehran Sahami Probability

78. Motivating Example

80. And The Revolution Starts…