Upload
charles-alvarez
View
214
Download
1
Tags:
Embed Size (px)
Citation preview
Intelligent Tutoring Intelligent Tutoring System based on Belief System based on Belief
networksnetworks
Maomi Ueno
Nagaoka University of Technology
Advantages of ITS in probabilistic approaches
Mathematical analysis of the system behaviors.
Mathematical approximation for convenient calculation
Decision making approachesto describe a teacher’s behavior
Assumption
A Teacher behaves to maximizes the following expected utility.
Expected Utility = ΣUtility×Probability
Probability model to describe human behaviors
Tversky、 A. and Kahneman,D. 197 3 Tversky、 A. and Kahneman,D. 197 4 Tversky、 A. and Kahneman,D. 19 83 Simon, H.A. 1974 and etc.
↓
It is impossible to describe human behaviors by using Probabilistic approaches.
Rationality
Human is Rational.(probabilistic approaches)
vs. Human is not Rational.(has pointed out,
and seems right.)
Purposes of this study
What is the utility of a teacher’s behavior? This paper tries to describe a teacher’s
behavior as a simple function.
Relational works Reye, J. (1986)“A belief net backbone for student
modeling”, Proc of Intelligent Tutoring System, pp.274-283.
R. Charles Murray and Kurt VanLehn (2000) “DD Tutor:A decision-Theoretic, Dynamic approach for Optimal Selection of Tutorial Actions”, Proc of Intelligent Tutoring System, pp. 153-162.
Unique features of this paper
A simple utility function:
Changes of the predictive student model Teacher’s Prior knowledge An exact parameterization of Bayesian
student modeling :
Predictive distribution of Bayesian networks.
Student model
Bayesian Belief networks
1
2
3
4
5
6
7
8 9
1011
12
13
14
15 application problem
ax + b =cx + d type
ax + bx = c type
ax + b= c type
x + a = b type
substituion representation of equation
ax = b type
division
multiplication
positive and negative number
addition
subtraction
literal representation
Figiure 1. An example of the student model
N
iiiN SxpSXXXP
121 ),|()|,,,(
},,,{ 21 iqi xxx ix },,,{ 21 iqxxx ix .i
Prior distribution as a Prior Knowledge
Dirichret distribution ,which is a conjecture distribution of the Bayesian networks
1
0
1'
1 11
0
1
0
)'(
)'()|(
k
nijk
N
i
q
j
kijk
kijk
SIJK
I
n
nSp
Predictive distribution as a student model
)''(
)'(
)]'([
)'()|(
1 ijkijk
q
jijkijkN
i ijk
ijk
nn
nn
n
nSp
i
X
Teacher’s actions
Instruction corresponding to the j’s node. Ask a question corresponding to the j’s
node.
Select the action to maximize utility function
n
i
iq
n
i
iq
lnn
linin
xxpxxp
actionxxpactionxxpEVII
1
1
2
111
2
111
),(log),(
)|,(log)|,(
Expected Value of Instruction Information
(EVII)
Stopping rule
EVII < 0.0001
Probability propagationGiven Instruction frame j
P(xj) →p(xj=1 | x1=1, x2=1, xj-1=1)=1
Given question frame j
P(xj) → xj =1 :right answer
0:wrong answer
Examples
Data: 248 Junior high school students test data
1
2
3
4
5
6
7
8 9
1011
12
13
14
15 application problem
ax + b =cx + d type
ax + bx = c type
ax + b= c type
x + a = b type
substituion representation of equation
ax = b type
division
multiplication
positive and negative number
addition
subtraction
literal representation
Figiure 1. An example of the student model
Prior parameter n1’ <n0’P(root) = 0.0
When a teacher know that the student knowledge is poor
Strategy
Bottom Up strategy
(from the easy material to the difficult material)
Instruction frames
Prior parameter n1’ >n0’P(top)=1
When a teacher know that the student knowledge is excellent,
Top down strategy
The system presents the difficult question. If the student provides wrong answer, then the system presents more easy question and instruction.
Prior parameter n1’ =n0’
When a teacher have no knowledge about the student knowledge
Flexible strategies
Quesion Frame 15
Question Frame 12
0.90.90.8
0.80.7
0.90.9
0.90.80.60.40.40.20.10.0 0.0
0.80.7
0.70.6
0.90.9
0.90.90.50.30.00.00.0
0.8QuestionFrame 9
0.1
0.80.7
0.70.6
0.90.9
1.00.90.50.30.00.10.1
0.9 QuestionFrame 3
0.1
10.9
0.90.8
0.90.9
1.00.90.60.40.00.10.1
1
QuestionFrame 11
0.1
10.9
0.90.9
0.90.9
1.00.90.91.00.00.10.1
1 Instruction Frame 12
0.1
10.9
0.90.9
0.90.9
1.00.90.91.01.00.60.4
Instruction Frame 13
0.7
10.9
0.90.9
0.90.9
1.00.90.91.01.01.00.8
Instruction Frame 14
0.8
10.9
0.90.9
0.90.9
1.00.90.91.01.01.01.0
Instruction Frame 15
1.0
10.9
0.90.9
0.90.9
1.00.90.91.01.01.01.0
Strategy
Diagnose the student knowledge states Then, the system instructs knowledge
which student can not understand by using the bottom-up strategy.
Conclusions
The prior knowledge for the student Prediction of student’s knowledge A simple utility function:
How can the teacher change the student’s predicted knowledge states.
Future tasks
We are developing large scale ITS based on this study.
How can we evaluate the behaviors of the system? Good or bad?