midterm review dr. bernard chen ph.d. university of central arkansas spring 2011

Midterm Review

Dr. Bernard Chen Ph.D.University of Central Arkansas

Spring 2011

Outline

Ch3 Structures and Strategies for State Space Search

Ch4 Heuristic Search Ch5 Stochastic Search

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

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

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

“tic-tac-toe” state space graph

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

State Space Representation

A goal in configuration in the 8-puzzle

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

State Space Representation

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

8-puzzle BFS

8-puzzle DFS

Outline

Ch3 Structures and Strategies for State Space Search

Ch4 Heuristic Search Ch5 Stochastic Search

Introduction 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

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

Introduction

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

Introduction

Introduction

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

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

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

Dynamic Programming (DP)

BAADDCABDDABBA_DC_B_ _A

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

Best First Search

Best First Search

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

Minimax Procedure on Exhaustively Search Graphs

State space for a variant of nim. Each state partitions the seven matches into one or more piles.

Minimax Procedure on Exhaustively Search Graphs

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

Minimax Procedure on Exhaustively Search Graphs

Exercises

Perform MINIMAX on the tree shown in Figure 4.30.

Exercises

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

Outline

Ch3 Structures and Strategies for State Space Search

Ch4 Heuristic Search Ch5 Stochastic Search

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.

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?

Exercises

Naïve Bayesian Classifier: Training Dataset

Class:C1:buys_computer = ‘yes’C2:buys_computer = ‘no’

Data sample X = (age <=30,Income = medium,Student = yesCredit_rating = Fair)

age income studentcredit_ratingbuys_computer<=30 high no fair no<=30 high no excellent no31…40 high no fair yes>40 medium no fair yes>40 low yes fair yes>40 low yes excellent no31…40 low yes excellent yes<=30 medium no fair no<=30 low yes fair yes>40 medium yes fair yes<=30 medium yes excellent yes31…40 medium no excellent yes31…40 high yes fair yes>40 medium no excellent no

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

Naïve Bayesian Classifier: An Example X = (age <= 30 , income = medium, student = yes,

credit_rating = fair)

P(X|Ci) :

P(X|buys_computer = “yes”) = 0.222 x 0.444 x 0.667 x 0.667 = 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”)

Naïve Bayesian Classifier: An Example

Test on the following example:

X = (age > 30, Income = Low, Student = yes Credit_rating = Excellent)

So how is “Tomato” pronounced

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

Outline

Expert System introduction Rule-Based Expert System

Goal Driven Approach Data Driven Approach

Model-Based Expert System

The Design of Rule-Based Expert System

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

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

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

A unreal Expert System Example Rule 1: if

the engine is getting gas, andthe engine will turn over,thenthe problem is spark plugs.

Rule 2: ifthe engine does not turn over, andthe lights do not come onthenthe problem is battery or cables.

Rule 3: ifthe engine does not turn over, andthe lights do come onthen the problem is the starter motor.

Rule 4: ifthere is gas in the fuel tank, andthere is gas in the carburetorthenthe engine is getting gas.

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

The production system after Rule 1 has fired.

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

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

Data-Driven Reasoning

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

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

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

NASA Example