Midterm Review

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Midterm Review

• Dr. Bernard Chen Ph.D.
• University of Central Arkansas
• Spring 2011

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Outline

• Ch3 Structures and Strategies for State Space
  Search
• Ch4 Heuristic Search
• Ch5 Stochastic Search

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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

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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

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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

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tic-tac-toe state space graph
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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

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State Space Representation

• A goal in configuration in the 8-puzzle

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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

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State Space Representation
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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

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8-puzzle BFS
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8-puzzle DFS
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Outline

• Ch3 Structures and Strategies for State Space
  Search
• Ch4 Heuristic Search
• Ch5 Stochastic Search

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Introduction

• George Polya defines heuristic as
• the study of the methods and rules of discovery
  and invention
• This meaning can be traced to the terms 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

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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

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Introduction
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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

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Introduction
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Introduction
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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

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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

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Dynamic Programming (DP)

_ B A A D D C A B D D A
_ 0 1 2 3 4 5 6 7 8 9 10 11
B 1 0 1 2 3 4 5 6 7 8 9 10
B 2 1 2 3 4 5 6 7 6 7 8 9
A 3 2 1 2 3 4 5 6 7 8 9 8
D 4 3 2 3 2 3 4 5 6 7 8 9
C 5 4 3 4 3 4 3 4 5 6 7 8
B 6 5 4 5 4 5 4 5 4 5 6 7
A 7 6 5 4 5 6 5 4 5 6 7 6
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Dynamic Programming (DP)
BAADDCABDDA BBA_DC_B_ _A
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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

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Best First Search
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Best First Search
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(No Transcript)
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Minimax Procedure on Exhaustively Search Graphs

• Lets 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 51 or
  42 but not 33
• The first player who can no longer make a move
  loses the game

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

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Minimax Procedure on Exhaustively Search Graphs

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Exercises

• Perform MINIMAX on the tree shown in Figure 4.30.

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Exercises

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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

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Outline

• Ch3 Structures and Strategies for State Space
  Search
• Ch4 Heuristic Search
• Ch5 Stochastic Search

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Bayes Theorem

• P(A), P(B) is the prior probability
• P(AB) is the conditional probability of A, given
  B.
• P(BA) is the conditional probability of B, given
  A.

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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?

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Exercises

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Naïve Bayesian Classifier Training Dataset
Class C1buys_computer yes C2buys_computer
no Data sample X (age lt30, Income
medium, Student yes Credit_rating Fair)
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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(XCi) for each class
• P(age lt30 buys_computer yes)
  2/9 0.222
• P(age lt 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

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Naïve Bayesian Classifier An Example

• X (age lt 30 , income medium, student yes,
  credit_rating fair)
• P(XCi)
• P(Xbuys_computer yes) 0.222 x 0.444 x
  0.667 x 0.667 0.044
• P(Xbuys_computer no) 0.6 x 0.4 x 0.2 x 0.4
  0.019
• P(XCi)P(Ci) P(Xbuys_computer yes)
  P(buys_computer yes) 0.028
• P(Xbuys_computer no)
  P(buys_computer no) 0.007
• Therefore, X belongs to class (buys_computer
  yes)

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Naïve Bayesian Classifier An Example

• Test on the following example
• X (age gt 30,
• Income Low,
• Student yes
• Credit_rating Excellent)

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So how is Tomato pronounced

• A probabilistic finite state acceptor for the
  pronunciation of tomato, adapted from Jurafsky
  and Martin (2000).

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Outline

• Expert System introduction
• Rule-Based Expert System
• Goal Driven Approach
• Data Driven Approach
• Model-Based Expert System

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The Design of Rule-Based Expert System

• architecture of a typical expert system for a
  particular problem domain.

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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

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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

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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
• then
• the problem is battery or cables.
• Rule 3 if
• the engine does not turn over, and
• the lights do come on
• then
• the problem is the starter motor.
• Rule 4 if
• there is gas in the fuel tank, and
• there is gas in the carburetor
• then

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

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The production system after Rule 1 has fired.

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

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

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Data-Driven Reasoning
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The production system after evaluating the first
premise of Rule 2, which then fails.

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

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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

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NASA Example