A Hidden Markov Model Approach to Predict Students' Actions in an Adaptive and Intelligent Web-Based Educational system

A Hidden Markov Model Approach to Predict Students' Actions in an Adaptive and Intelligent Web-Based Educational system
International Conference on Information & Communications Technologies from Theory to Applications –ICTTA -08, 06-10 April 2008, Damascus-Syria
A Hidden Markov Model Approach to
Predict Students' Actions in an
Adaptive and Intelligent Web-Based
Educational system
Masun Nabhan Homsi
University of Aleppo
SYRIA
Dr.Rania LUTFI
University of Al-Baath
SYRIA
Prof. Dr Ghias BARAKAT
University of Aleppo
SYRIA
Dr. Rosa María Carro Salas
Universidad Autónoma de
Madrid

Overview
• Introduction.
• Prediction Process:
– Initialization Phase.
– Adjustment Phase.
– Prediction Phase.
• Prediction algorithm.
• Implementation & Results.
• Conclusions.
• Future works.

Introduction
The system consists of five
Components:
• Domain model
• Student model
• Pedagogical module
• Interface module
• Prediction Module
AIWBES
Domain
Model
Pedagogic
al Module
Student
Model
Interface
NN-HMM
XML-DTD
Prediction
Module
•AIWBESs try to be more adaptive than traditional educational
systems "Just-put-it-on-the-web" by building a student model to
represent goals, preferences and knowledge of each student and
updating it in accordance with their knowledge acquisition
process.

HMM
, A, B
Prediction Module
It consists of 3 phases :
– Initialization Phase
– Adjustment Phase
– Prediction Phase
InitializationInitialization
Adjustment Prediction
Concepts
sequence
HMM
, A, B
New concepts'
sequence
Next
concept
General prediction process

Initialization Phase
• N, the number of hidden states S= {S0, S1, …, SN-1), which
represents number of concepts in the domain model of the system.
qt represents the hidden state at time t.
• M, the number of observable states, with V = {V0, V1, …, VM-1} the
set of observable states (Symbols), and Ot the observation state at
time t.
• A={aij}, the transition probabilities between hidden states Si and Sj.
• B={bj(k)}, the probabilities of the observable states Vk in hidden
states Sj.
• ∏={i}, the initial hidden state probabilities.
AIWBES
Compute
, A, B
HMM
(λ)
Student
C01, C05, C11, …
Concepts' Sequence

Adjustment Phase
• t(i): the forward variable
• t(i) : the backward variable
• t(i, j): the probability of being in hidden state Si at time t
and making a transition to state Sj at time t+1, given the
observation sequence O= O1, O2, …, OT and the model
=(A, B, ).
• t(i) :the probability of being in state Si at time t given the
observation sequence O= O1, O2, …, OT and the model
=(A, B, ).
AIWBES
C05, C011,…,C03
New Concepts'
Sequence
Compute
, 
Compute
, 
Compute
BA,,
HMM

HMM
λ

Initialization & Adjustment Phases
1. For each student a HMM =(A, B, ) is
Initialized;
2. Compute t(i), t(i), t(i, j), t(i), t=1…,T, i-
0,…,N-1, j=0,…,N-1;
3. Adjust the model =(A, B, ) to get .
4. If P(O|) - P(O|)<Δ then stop.
5. Else set =  and go to 2.

Prediction Phase


Concepts
C01
C02
CN
Get
maximum
Probability
to predict
next
concept will
be visited
by the
student
C05,
C011,…,C03
New
Concepts'
Sequence
.
.
.
.
.
.
01C,03,…,C011, C05C
02C,03,…,C011, C05C
CN,03,…,C011, C05C
HMM


HMM


HMM

Forward
Algorithm
Forward
Algorithm
Forward
Algorithm
•The Forward Algorithm is applied to determine the probability distribution
of each concept (state) in the course.
•The highest value represents the next concept will be visited by the
student.

Implementation and Results (1)
Code Concept
C01 Verb to be-Positive Form
C02 Verb to be-Negative Form
C03 Verb to be-Question Form
… …
C42 Simple Future tense-Short and Long answers
Navigation sequence
C05 C06 C07 C08 C01 C02 C03 C04 C09 C10 …Student 1
Numbers
1- 10
Numbers
11- 20
Numbers
21-1000
Ordinal
numbers
Verb to be
Negative Form
Verb to be
Question Form
Verb to be
Short/Long answer
Simple Present Tense
Positive Form
? ? …
Verb to be
Positive Form
Negative Form

• A={aij}, the transition probabilities between
hidden states Si and Sj, are randomly initialized
to approximately 1/N, each row summing to 1.
• B={bj(k)}, the probabilities of the observable
states Vk in hidden states Sj. are randomly
initialized to approximately 1/M, each row
summing to 1.
• ∏={i}, the initial hidden state probabilities, are
randomly set to approximately 1/N, their sum
being 1.

C05 C06 C07 C08 C01 C02 C03 C04 C09 C10
Where
should I
go?
C01 C02 C03 C11 C41 C42
HMM1 HMM2 HMM3 HMM11 HMM41 HMM42… …
0.025 0.013 0.070 0.090 0.083 8.065… …

Code Concept
C01 Verb to be-Positive Form
C02 Verb to be-Negative Form
C03 Verb to be-Question Form
… …
C42 Simple Future tense-Short and Long answers
Navigation sequence
Negative Form
Short/Long Form …Offering, accepting
and refusing
Numbers
1- 10
Numbers
11- 20
Numbers
21-1000
Ordinal
numbers
Verb to be
Positive Form
Verb to be
Negative Form
Verb to be
Question Form
Verb to be
Short/Long answer
Positive Form
Negative Form

A screenshot of HMM
predictor.

Teacher's page to guide
students.

Figure 5. A screenshot of HMM predictor
Suggestion list
A screenshot of
suggestion list.

Recall (sensitivity)= Precision =
TP
TP+ FP
Predicted Concept
NegativePositive
False
Negative
(FN)
True Positive
(TP)
PositiveConcepts
True Negative
(TN)
False Positive
(FP)
Negative
TP
TP+ FN

Testing results of various experiments

The relation between recall and precision

Conclusions
• This paper shows how Hidden Markov Model
is very suitable for predicting students'
navigation actions within an AIWBES for
teaching EFL.
• The initial experiments show that the
concept prediction results can simulate
teacher guidance to students to find
appropriate information more efficiently
and accurately.

Future Work
• Prediction module needs to be evaluated
by a larger students' groups with the
objective to increase prediction latencies.
• Make several comparisons of results
among variations of student models using
Viterbi algorithm or Neural networks

-University of Aleppo
ِ◌
- Al-Baath University
-Universidad Autónoma de Madrid

A Hidden Markov Model Approach to Predict Students' Actions in an Adaptive and Intelligent Web-Based Educational system

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