# Comparative Analysis of Exemplar-Based Approaches for Students' Learning Style Diagnosis Purposes
## 2 Methods
### Proposed Approach for Students' Learning Style Prediction  
#### 2.6.1 Bayesian Case Model for Students' Learning Style Modelling  
When applying the Bayesian approach for student's learning style identification, learning style is considered as latent parameter of interest \(\mathrm{\theta}\), and student's log consisting of his/her behavioral activities is considered as an observation \(\mathrm{x_{i}}\). \(\mathrm{X}=\{\mathrm{x_{i}},\ldots,\mathrm{x_{n}}\}\) will be a set of complete observations from a density that depends on \(\mathrm{\theta}:\pi(\mathrm{x}|\mathrm{\theta})\). According to the [PERSON] theorem, inference on the conditional probability of student's learning style is based on posterior  
augmentation [49]. One or some parameters (called nuisance parameters) may be eliminated by integrating them out, i.e., marginalizing (focusing on the sums of distributions in the margin) over the distribution of the variables being discarded. Gibbs sampler, which integrates out (marginalizes over) one or more variables when sampling for some other variable, is called collapsed Gibbs sampler. Model-based student learning style clustering is based on a finite mixture of distributions, in which each mixture component is taken to correspond to a different learning style cluster. The LDA framework models a per-cluster distribution of behavioral activities of the student, helping to understand what cluster each activity might be referring to. LDA treats each learning style cluster assignment as a multinomial random variable drawn from a symmetric Dirichlet and logistic normal prior. Inference algorithms build the latent space, a collection of learning styles for the corpus and a collection of learning style proportions for each of its logs. Mixed membership models allow each student's log to exhibit multiple components, where each component is a distribution over behavioral activities. Conditioned on collection, inspecting the posterior of the components reveals the \"learning styles\" inherent in the logs, i.e., the significant patterns of activities associated under a single learning style [42]. In the case of exemplar-based dynamic modeling of students' learning style using BCM, the model could generate student learning style clusters based on historical data about the student's behavioral activities in a virtual learning environment. A principal diagram depicting BCM application for modelling students' learning style using students' behavioral data in virtual learning environment is presented in Figure 2. First, data mining of students' logs stored in a virtual learning environment (VLE) must be done. The result of the data mining procedure should be a set of logs each consisting of a particular student's behavioral activities in a virtual learning environment. Each log should be presented as bag of independent data objects, i.e., student's behavioral activities that reflect his/her learning style (data objects are correlated in some way, representing the student's learning style). Data mining methods were explored and described by authors in [50], but this paper focuses on BN + CBR modelling only. In students' leaning style model, which is a model of high-dimensional discrete data, we model student behavioral activity data in a virtual learning environment as coming from a mixture distribution, with mixture components corresponding to learning style clusters. We use the following notions. Observation is log with student's behavioral activities stored. Having groups of observations, each group is modeled with a mixture. Components are distributions over the vocabulary of behavioral activities (recurring patterns of observed activities). The posterior components look like learning styles (distributions that place their mass on behavioral activities that exhibit a learning style). Probabilities associated with each component are called the mixture weights. The mixture components (the individual distributions that are combined to form the mixture distribution) are shared across groups.