**3. Learner modeling**

**2.2. Bayesian networks**

*2.2.1. Definition*

information.

Before describing our investigation of the use of Bayesian networks in learner modeling, we'll

In the rest of this section, we'll take a typology of nodes inspired by Conati [5], and found in different terms in the literature. The field layer is the set of nodes modeling epistemic knowl‐ edge of the learner, and the task layer is the set of nodes modeling the actions of the learner.

Numerous models have been created through the representation of knowledge. Probabilistic graphical models, and especially Bayesian networks initiated by Pearl [6] in the 1980s, have proven to be useful tools for representing uncertain knowledge and reasoning from incomplete

A Bayesian network is a directed acyclic graph in which the nodes correspond to the variables (user properties), and the links represent probabilistic relationships of influence. These variables can belong to the field of knowledge, the base knowledge and / or the cognitive model. Each node represents the system's belief about possible values (levels, states) of the variable. Thus, the conditional probability distribution must be specified for each node. If the

The graph is also called the "structure" of the model, and the probability tables are its "param‐ eters". They can be provided by experts, or calculated from data; generally speaking, the structure is defined by experts and the calculated parameters are from experimental data.

*G* =(*X* , *E*), an acyclic directed graph with various vertices associated with a set of random variables *X* =(*X* , ..., *Xn*) ;N= {P(Xi | Pa(Xi))} All the probabilities of each node *Xi* are con‐

According to Mayo [7], a Bayesian network allows compact representation of the joint

1 P(X1,X2, · · · ,Xn) P(Xi | Pa(Xi)) *n*

*i*= <sup>=</sup> Õ

These methods obviously use the concept of conditional probability, i.e., what is the probability of *Xi* knowing that I have observed *Xj* ; but they also use the Bayes theorem, which calculates,

To specify a Bayesian network in a comprehensive way, it is necessary, as we have seen in the definition, to specify the network structure (the acyclic graph) and the network parameters

conversely, the probability of *Xj* knowing *Xi*, when P(Xi | Xj) is known.

define such networks and address the meaning of inference in this context.

168 E-Learning - Instructional Design, Organizational Strategy and Management

variables are discrete, they can be presented as a table.

Consider a Bayesian network *B* =(*G*, *N* ) defined by

ditional to the state of its parents Pa(Xi) in G.

probability distribution over a set of variables:

*2.2.2. Bayesian network construction*

In this section, we present the steps to follow when modeling the learner in an adaptive educational system, beginning with the user meta-model and then moving to use of the case diagram, and regrouping all actions of the learner in an adaptive system.

### **3.1. The metamodel**

Here we discuss a specific user meta-model for e-learning, as presented by Aammou [8]. This model features a combination of models for e-learning and adaptive hypermedia. It takes into account elements, such as the history of actions that are missing in formal models. The construction of this model allows us to understand the user's creative process model for adaptive hypermedia, helping us to build our hypernym model.

In our user model for e-learning, we want to be able to:


is such that when the user wishes to come back to a concept already brought to his attention, he is presented with documents that are the same as those from his first learning of the concept.

The UML class diagram representation of our user model is given in Fig. 2.

**Figure 2.** UML class diagram representing the user metamodel


The classes of Document and Concept are detailed in the model domain.

#### **3.2. The use case diagram**

is such that when the user wishes to come back to a concept already brought to his attention, he is presented with documents that are the same as those from his first learning of the

**•** The **User Manager** class is responsible for interfacing with the other components of adaptive hypermedia systems. For this purpose, the Ask and Tell methods are used to ask questions and provide answers to the external components (domain model, adaptation model). The User Manager class is connected to all users, and is responsible for managing by an

**•** The **User** class is responsible for representing information pertaining to a particular user. It

**•** The **Attribute Preference** class is responsible for representing the preferences of the user. These are view preferences: font size, color problems, contrasts, etc., as well as presentation preferences. The user may prefer textual or graphic elements, and may not want an audio

**•** The **Attribute Background** class is responsible for representing the user attributes related

is composed of predefined attributes: name, username, password and age.

The UML class diagram representation of our user model is given in Fig. 2.

170 E-Learning - Instructional Design, Organizational Strategy and Management

**Figure 2.** UML class diagram representing the user metamodel

aggregation relationship.

element, for example.

to academic / professional background.

concept.

Based on the meta-model, we were able to map out the functionality of the learner using the use case diagram (Fig. 3) to reflect a portion of the student's actions in an adaptive system. In this section, we will explain each of these actions, and consider the relationships of these actions with each other and within the system operation process.

Based upon the meta-model presented in the previous section, we have illustrated a learner's actions in a learning situation in an adaptive educational system (Table 1).



**Table 1.** The mains actions of a learner in a learning situation in an adaptive system

In Fig. 3, a main actor is identified, named "the learner". The figure shows the generalization relationships between use cases and the learner, and the generalization relationships of inclusion and extension between use cases.

**Figure 3.** Use case diagram UML representing the learner actions

In particular, the functional requirement of "Learner" represents all information about the learner in the hypermedia system (the learner's knowledge, skills, personal information, etc.). This functional requirement is shown with a generalization relationship with three functional requirements:


In the case of remediation, the functional requirement "Remediation" involves activation of the functional requirement "Call Tutor" through an inclusion relation. This requirement represents activation of the tutor to help the student to return to shortcomings in the learning activity.

Another inclusion relation is represented in Fig. 3. The actions of the learner in an adaptive system are represented, appearing in the relationship between the functional requirement "Call Tutor" and the requirement of "Reading the History of the Learner", which activates the return of the system to the profile and the learner's course information. The requirement "System Awareness" enables the system to follow the course of the learner after remediation.
