1. Dr. Bernard Chen Ph.D. University of Central Arkansas Spring 2011
Midterm Review
Dr. Bernard Chen Ph.D.
University of Central Arkansas
Spring 2011

2. Outline Ch3 Structures and Strategies for State Space Search
Ch4 Heuristic Search
Ch5 Stochastic Search

3. Introduction to Representation
The representation function is to capture the critical features of a problem and make that information accessible to a problem solving procedure
Expressiveness (the result of the feature abstracted) and efficiency (the computational complexity) are major dimensions for evaluating knowledge representation

4. Introduction to Search
Given a representation, the second component of intelligent problem solving is search
Human generally consider a number of alternatives strategies on their way to solve a problem
Such as chess
Player reviews alternative moves, select the “best” move
A player can also consider a short term gain

5. Introduction to Search
We can represent this collection of possible moves by regarding each board as a state in a graph
The link of the graph represent legal move
The resulting structure is a state space graph

6. “tic-tac-toe” state space graph

7. State Space Representation
State space search characterizes problem solving as the process of finding a solution path form the start state to a goal
A goal may describe a state, such as winning board in tic-tac-toe

8. State Space Representation
A goal in configuration in the 8-puzzle

9. State Space Representation
The Traveling salesperson problem
Suppose a salesperson has five cities to visit and then must return home
The goal of the problem is to find the shortest path for the salesperson to travel

10. State Space Representation

11. BFS and DFS
In addition to specifying a search direction (data-driven or goal-driven), a search algorithm must determine the order in which states are examined in the graph
Two possibilities:
Depth-first search
Breadth-first search

12. 8-puzzle BFS

13. 8-puzzle DFS

14. Outline Ch3 Structures and Strategies for State Space Search
Ch4 Heuristic Search
Ch5 Stochastic Search

15. Introduction IN AI, heuristics are formalized as
George Polya defines heuristic as:
“the study of the methods and rules of discovery and invention”
This meaning can be traced to the term’s Greek root, the verb eurisco, which means “I discover”
When Archimedes emerged from his famous bath clutching the golden crown, he shouted “Eureka!!”, meaning I have found it
IN AI, heuristics are formalized as
Rules for choosing those branches in a state space that are most likely to lead to an acceptable problem solution

16. Introduction Consider heuristic in the game of tic-tac-toe
A simple analysis put the total number of states for 9!
Symmetry reduction decrease the search space
Thus, there are not 9 but 3 initial moves:
to a corner
to the center of a side
to the center of the grid

17. Introduction

18. Introduction
Use of symmetry on the second level further reduces the number of path to 3* 12 * 7!
A simple heuristic, can almost eliminate search entirely: we may move to the state in which X has the most winning opportunity
In this case, X takes the center of the grid as the first step

19. Introduction

20. Introduction

21. Hill-Climbing
The simplest way to implement heuristic search is through a procedure called hill-climbing
It expend the current state of the search and evaluate its children
The Best child is selected for further expansion
Neither it sibling nor its parent are retained
Tic-Tac-Toe we just saw is an example

22. Dynamic Programming (DP)
DP keeps track of and reuses of multiple interacting and interrelated subproblems
An example might be reuse the subseries solutions within the solution of the Fibonacci series
The technique of subproblem caching for reuse is sometimes called memorizing partial subgoal solutions

23. Dynamic Programming (DP)_ B A D C 1 2 3 4 5 6 7 8 9 10 11

24. Dynamic Programming (DP)
BAADDCABDDA
BBA_DC_B_ _A

25. Best First Search
For the 8-puzzle game, we may add 3 different types of information into the code:
The simplest heuristic counts the tiles out of space in each state
A “better” heuristic would sum all the distances by which the tiles are out of space

26. Best First Search

27. Best First Search

29. Minimax Procedure on Exhaustively Search Graphs
Let’s consider a variant of the game nim
To play this game, a number of tokens are placed on a table between the two players
At each move, the player must divide a pile of tokens into two nonempty piles of different sizes
Thus, 6 tokens my be divided into piles of 5&1 or 4&2 but not 3&3
The first player who can no longer make a move loses the game

30. Minimax Procedure on Exhaustively Search Graphs
State space for a variant of nim. Each state partitions the seven matches into one or more piles.

31. Minimax Procedure on Exhaustively Search Graphs

32. Minimax Procedure on Exhaustively Search Graphs
Minimax propagates these values up the graph through successive parent nodes according to the rule:
If the parent is a MAX node, give it the maximum value among its children
If the parent is a MIN node, give it the minimum value among its children

33. Minimax Procedure on Exhaustively Search Graphs

34. Exercises
Perform MINIMAX on the tree shown in Figure 4.30.

35. Exercises

36. Exercises Consider 3D tic-tac-toe.
How to represent state search space?
Analysis the complexity of the state space?
Propose a heuristic for playing this game

37. Outline Ch3 Structures and Strategies for State Space Search
Ch4 Heuristic Search
Ch5 Stochastic Search

38. Bayes’ Theorem P(A), P(B) is the prior probability
P(A|B) is the conditional probability of A, given B.
P(B|A) is the conditional probability of B, given A.

39. Exercises
Suppose an automobile insurance company classifies a driver as good, average, or bad.
Of all their insured drivers, 25% are classified good, 50% are average, and 25% are bad.
Suppose for the coming year, a good driver has a 5% chance of having an accident, and average driver has 15% chance of having an accident, and a bad driver has a 25% chance.
If John had an accident in the past year what is the probability that John are a good driver?

40. Exercises

41. Naïve Bayesian Classifier: Training Dataset
C1:buys_computer = ‘yes’
C2:buys_computer = ‘no’
Data sample
X = (age <=30,
Income = medium,
Student = yes
Credit_rating = Fair)

42. Naïve Bayesian Classifier: An Example
P(Ci): P(buys_computer = “yes”) = 9/14 = 0.643
P(buys_computer = “no”) = 5/14= 0.357
Compute P(X|Ci) for each class
P(age = “<=30” | buys_computer = “yes”) = 2/9 = 0.222
P(age = “<= 30” | buys_computer = “no”) = 3/5 = 0.6
P(income = “medium” | buys_computer = “yes”) = 4/9 = 0.444
P(income = “medium” | buys_computer = “no”) = 2/5 = 0.4
P(student = “yes” | buys_computer = “yes) = 6/9 = 0.667
P(student = “yes” | buys_computer = “no”) = 1/5 = 0.2
P(credit_rating = “fair” | buys_computer = “yes”) = 6/9 = 0.667
P(credit_rating = “fair” | buys_computer = “no”) = 2/5 = 0.4

43. Naïve Bayesian Classifier: An Example
X = (age <= 30 , income = medium, student = yes, credit_rating = fair)
P(X|Ci) :
P(X|buys_computer = “yes”) = x x x = 0.044
P(X|buys_computer = “no”) = 0.6 x 0.4 x 0.2 x 0.4 = 0.019
P(X|Ci)*P(Ci) : P(X|buys_computer = “yes”) * P(buys_computer = “yes”) = 0.028
P(X|buys_computer = “no”) * P(buys_computer = “no”) = 0.007
Therefore, X belongs to class (“buys_computer = yes”)

44. Naïve Bayesian Classifier: An Example
Test on the following example:
X = (age > 30,
Income = Low,
Student = yes
Credit_rating = Excellent)

45. So how is “Tomato” pronounced
A probabilistic finite state acceptor for the pronunciation of “tomato”, adapted from Jurafsky and Martin (2000).

46. Outline Expert System introduction Rule-Based Expert System
Goal Driven Approach
Data Driven Approach
Model-Based Expert System

47. The Design of Rule-Based Expert System
architecture of a typical expert system for a particular problem domain.

48. Strategies for state space search
In data driven search, also called forward chaining, the problem solver begins with the given facts of the problem and set of legal moves for changing state
This process continues until (we hope!!) it generates a path that satisfies the goal condition

49. Strategies for state space search
An alternative approach (Goal Driven) is start with the goal that we want to solve
See what rules can generate this goal and determine what conditions must be true to use them
These conditions become the new goals
Working backward through successive subgoals until (we hope again!) it work back to

50. A unreal Expert System Example
Rule 1: if
the engine is getting gas, and
the engine will turn over,
then
the problem is spark plugs.
Rule 2: if
the engine does not turn over, and
the lights do not come on
the problem is battery or cables.
Rule 3: if
the lights do come on
the problem is the starter motor.
Rule 4: if
there is gas in the fuel tank, and
there is gas in the carburetor
the engine is getting gas.

51. The production system at the start of a consultation in the car
The production system at the start of a consultation in the car diagnostic example.

52. The production system after Rule 1 has fired.

53. The system after Rule 4 has fired
The system after Rule 4 has fired. Note the stack-based approach to goal reduction.

54. The and/or graph searched in the car diagnosis example, with the conclusion of Rule 4 matching the first premise of Rule 1.

55. Data-Driven Reasoning

56. The production system after evaluating the first premise of Rule 2, which then fails.

57. The data-driven production system after considering Rule 4, beginning its second pass through the rules.

58. Model-Based Expert System
A more robust, deeply explanatory approach would begin with a detailed model of the physical structure of the circuit and equations describing the expected behavior of each component and their interactions.
A knowledge based reasoner whose analysis is founded directly on the specification and functionality of a physical system is called a MODEL-BASED System

59. NASA Example