1. © Daniel S. Weld 1 Midterm Search Space Bayes Net Learning / Cross Validation Lessons for the Final I’ll hit these areas again I’ll include one midterm problem verbatim Likely others with small changes

2. © Daniel S. Weld 2 Bayes Nets Since a high-stakes murder case revolves on a DNA sample found near the murder scene, the sample is sent to two different labs. Each lab uses it’s own machine to determine if there is a match (events M1 and M2). The accuracy of each machine depends on whether it is calibrated (C1 and C2). The judge hires you to analyze the situation, specifically to advise on the guilt, G, of the suspect.

3. © Daniel S. Weld 3 Structures Two astronomers in Chile & Alaska measure (M1, M2) the number (N) of stars. Normally there is a chance of error, e, of under or over counting by 1 star. But sometimes, with probability f, a telescope can be out of focus (events F1 and F2) in which case the affected scientist will undercount by 3 stars F1F1 F2F2 M1M1 M2M2 N F1F1 F2F2 M1M1 M2M2 N F1F1 F2F2 M1M1 M2M2 N

4. © Daniel S. Weld 4 Cross validation Partition examples into k disjoint equiv classes Now create k training sets Each set is union of all equiv classes except one So each set has (k-1)/k of the original training data  Train  Test

5. © Daniel S. Weld 5 Cross Validation Partition examples into k disjoint equiv classes Now create k training sets Each set is union of all equiv classes except one So each set has (k-1)/k of the original training data Test

6. © Daniel S. Weld 6 Cross Validation Partition examples into k disjoint equiv classes Now create k training sets Each set is union of all equiv classes except one So each set has (k-1)/k of the original training data Test

7. © Daniel S. Weld 7 Search You are given 12 seemingly identical coins and a two-pan scale. One of the coins is lighter than or heavier than the others. Using the scale, you must identify the bogus coin and determine if it is lighter than or heavier than the others; You are allowed to do at most 3 measurements. Describe this challenge as a search problem

8. © Daniel S. Weld 8 Search States Partial “plans” to test the coins Operators Plan modification operators (e.g. adding a measurement)

9. © Daniel S. Weld 9 Need Two Viewpoints Belief State of Agent Initially 24 possible world states: Coin A … L is bogus x {heavy, light} Plan of Agent And / or tree measure A vs B … AB vs CD … ABCD vs EFGH <> = A l B l C l D l E h F h G h H h A h B h C h D h E l F l G l H l I l I h J l J h K l K h L l L h

10. © Daniel S. Weld 10 Operators measure ABCD vs EFGH <> = A l B l C l D l E h F h G h H h measure A vs B … AB vs CD … ABE vs CDF <> =

11. © Daniel S. Weld 11 Administrivia Reading for today’s class: ch 5 Reading for next Tues: ch 22 Problem Set Out soon Programming?

12. © Daniel S. Weld 12 Activity Recognition Natural Language 573 Core Topics Agency Problem Spaces Search Knowledge Representation Reinforcement Learning Inference Planning Classical, MDP, POMDP Supervised Learning Logic-Based Probabilistic

13. Constraint Satisfaction CSE 573 University of Washington

14. © Daniel S. Weld 14 Outline Problem spaces Search Blind Informed Local Heuristics & Pattern DBs for Constraint satisfaction       Definition Factoring state spaces Backtracking policies Variable-ordering heuristics Preprocessing algorithms

15. © Daniel S. Weld 15 Constraint Satisfaction Kind of search in which States are factored into sets of variables Search = assigning values to these variables Structure of space is encoded with constraints Backtracking-style algorithms work E.g. DFS for SAT (i.e. DPLL) But other techniques add speed Propagation Variable ordering Preprocessing

16. © Daniel S. Weld 16 Chinese Food as Search? States? Operators? Start state? Goal states? Partially specified meals Add, remove, change dishes Null meal Meal meeting certain conditions (rating?)

17. © Daniel S. Weld 17 Factoring States Rather than state = meal Model state’s (independent) parts, e.g. Suppose every meal for n people Has n dishes plus soup Soup = Meal 1 = Meal 2 = … Meal n = Or… physical state = X coordinate = Y coordinate =

18. © Daniel S. Weld 18 Chinese Constraint Network Soup Total Cost < $30 Chicken Dish Vegetable RiceSeafood Pork Dish Appetizer Must be Hot&Sour No Peanuts No Peanuts Not Chow Mein Not Both Spicy

19. © Daniel S. Weld 19 CSPs in the Real World Scheduling space shuttle repair Airport gate assignments Transportation Planning Supply-chain management Computer configuration Diagnosis UI optimization Etc...

20. 20 [Gajos & Weld, IUI-04] [Gajos et al., CHI-08] Adapting to Devices

21. © Daniel S. Weld 21 Supple Problem Formulation + Hierarchy of State Vars + Methods Screen Size, Available Widgets & Interaction Modes Func. Interface Spec. Device Model User Trace Custom Interface Rendering + Model of an Individual User’s Behavior (or that of a Group) { … } Approaches: Templates Expert System Optimization

22. Functional Spec. Typed DAG… Not Tree Interior Nodes  Container Types Leaves  Simple Types + Device Model User Trace Custom Interface Rendering + Func. Interface Spec.

23. © Daniel S. Weld 23 Add supple

24. © Daniel S. Weld 24 Binary Constraint Network Set of n variables: x 1 … x n Value domains for each variable: D 1 … D n Set of binary constraints (also “relations”) R ij  D i  D j Specifies which value pairs (x i, x j ) are consistent V for each country Each domain = 4 colors R ij enforces 

25. © Daniel S. Weld 25 Binary Constraint Network Partial assignment of values = tuple of pairs {...(x, a)…} means variable x gets value a... Tuple=consistent if all constraints satisfied Tuple=full solution if consistent + has all vars Tuple {(x i, a i ) … (x j, a j )} = consistent w/ a set of vars {x m … x n } iff  a m … a n such that {(x i, a i )…(x j, a j ), (x m, a m )…(x n, a n )} } = consistent

26. © Daniel S. Weld 26 N Queens As a CSP? Variables? Domain? Constraints?

27. © Daniel S. Weld 27 N Queens Variables = board columns Domain values = rows R ij = {(a i, a j ) : (a i  a j )  (|i-j|  |a i -a j |) e.g. R 12 = {(1,3), (1,4), (2,4), (3,1), (4,1), (4,2)} Q Q Q {(x 1, 2), (x 2, 4), (x 3, 1)} consistent with (x 4 )? Shorthand: “{2, 4, 1} consistent with x 4 ” {(x 1, 2), (x 2, 4), (x 3, 1)} consistent with (x 4 ) ? Shorthand: “{2, 4, 1} consistent with x 4 ”

28. © Daniel S. Weld 28 Cryptarithmetic SEND + MORE ------ MONEY State Space Set of states Operators [and costs] Start state Goal states Variables? Domains (variable values)? Constraints?

29. © Daniel S. Weld 29 Classroom Scheduling Variables? Domains (possible values for variables)? Constraints?

30. © Daniel S. Weld 30 CSP as a search problem? What are states? (nodes in graph) What are the operators? (arcs between nodes) Initial state? Goal test? Q Q Q

31. © Daniel S. Weld 31 Chronological Backtracking (BT) (e.g., depth first search) Q Q Q Q Q Q Q Q Q Q Q 1 2 3 4 5 6 Consistency check performed in the order in which vars were instantiated If c-check fails, try next value of current var If no more values, backtrack to most recent var

32. © Daniel S. Weld 32 Backjumping (BJ) Similar to BT, but more efficient when no consistent instantiation can be found for the current var Instead of backtracking to most recent var… BJ reverts to deepest var which was c-checked against the current var BJ Discovers (2, 5, 3, 6) inconsistent with x 6 No sense trying other values of x 5 Q Q Q Q Q

33. © Daniel S. Weld 33 5 Conflict-Directed Backjumping (CBJ) More sophisticated backjumping behavior Each variable has conflict set CS Set of vars that failed c-checks w/ current val Update this set on every failed c-check When no more values to try for x i Backtrack to deepest var, x d, in CS(x i ) And updateCS(x d ):=CS(x d )  CS(x i )-{x d } CBJ Discovers (2, 5, 3) inconsistent with {x 5, x 6 } Q Q Q Q Q 1 1 3 2 3 3 3 2 1 2 3 4 5 6 x1x1 x2x2 x3x3 x4x4 x5x5 x6x6 CS(x 5 ) 1,2,3 CS(x 6 ) 1, 2,3,5 Too complex to explain (Animation may be incorrect)

34. © Daniel S. Weld 34 BT { vs. BJ vs. CBJ Consistent node Inconsistent node

35. © Daniel S. Weld 35 Forward Checking (FC) Perform Consistency Check Forward Whenever a var is assigned a value Prune inconsistent values from As-yet unvisited variables Backtrack if domain of any var ever collapses Q Q Q Q Q FC only visits consistent nodes but not all such nodes skips (2, 5, 3, 4) which CBJ visits But FC can’t detect that (2, 5, 3) inconsistent with {x 5, x 6 }

36. © Daniel S. Weld 36 Number of Nodes Explored BT=BM BJ=BMJ=BMJ2 CBJ=BM-CBJ FC-CBJ FC More Fewer =BM-CBJ2

37. © Daniel S. Weld 37 Number of Consistency Checks BMJ2 BT BJ BMJ BM-CBJ CBJ FC-CBJ BM BM-CBJ2 FC More Fewer

38. © Daniel S. Weld 38 Crosswords