## 5 Proposed Semi-Supervised Regression Wrapper Scheme  
Semi-Supervised Learning (SSL) is a rapidly evolving subfield of ML, embracing a wide range of high-performance algorithms. Typically, an ML model \(h\) is built from a training dataset \(D=L\cup U\) consisting of a small pool of labeled examples \(L=\{x_{i},\ y_{i}\}_{i=1}^{l}\) and a large pool of unlabeled ones \(U=\{x_{i}\}_{i=1}^{u}\), \(l<u\), \(x_{i}\in X\), \(y_{i}\in\mathcal{Y}\), \(L\cap U=\varnothing\), without human intervention [45]. Depending upon the nature of the output attribute SSL is divided into two settings [9]:  
* Semi-Supervised Classification (SSC). The labels \(y_{i}\) of the output attribute are discrete, i.e., \(\mathcal{Y}=\{y_{1},y_{2},\ldots,y_{n}\}\). * Semi-Supervised Regression (SSR). The labels \(y_{i}\) of the output attribute are real, i.e., \(\mathcal{Y}\subseteq\mathbb{R}\). In our case, we employed an SSR scheme for exploiting the existence of both labeled and unlabeled data trying to acquire accurate estimations of the target attribute--students' final grade--based on a set of readily available data. Thus, one or more regressors are trained iteratively via selecting the most appropriate unlabeled data and annotating their missing target value in an automated fashion. Of course, the initial hypothesis is formatted on the manually gather the subset of \(L\). Furthermore, the fact that the training set is split into two disjoint subsets, \(L\) and \(U\), and that we aim at applying our trained model on another subset--the test set--which does not overlap with the training set leads us to an inductive SSR algorithm. The most representative algorithm found in the literature that seems to satisfy our ambitions is the COREG that was firstly proposed by [PERSON] [25]. Actually, this learning scheme constitutes the analog of the co-training scheme also based on disagreement rule in the case of SSC [46], inserting a local-based criterion for measuring the effectiveness of the candidate unlabeled instances into the currently trained model for completing a regression task. Although various criteria have been designed in the context of SSC [47; 48], the corresponding essential stage during an inductive SSR algorithm has not been highly studied by the related research community, following variants of the same criterion proposed in the case of COREG or proposing some new metrics that are mainly used under single-view works [44; 49; 50]. More specifically, the main concern of inductive SSR algorithms during the annotation of unlabeled examples is their _consistency_ with the already existing labeled instances. This property is examined by measuring the next formula:  
\[Consistency_{x_{j}}=\sum_{x_{i}\in L}\bigl{(}f(y_{i},h(x_{i}))-f\bigl{(}y_{i},h (\hat{x}_{i})\bigr{)}\bigr{)},\ \forall x_{j}\in U \tag{3}\]  
where \(f\) is a suitable performance metric, \(y_{i}\) is the actual value of the \(x_{i}\) labeled example, while \(h(x_{i})\) and \(h(\hat{x}_{i})\) denote the output of regressor \(h\) when is trained solely on the current labeled set and on the augmented labeled set with the currently examined \(x_{j}\) example, respectively. According to the COREG algorithm, a local criterion is inserted for investigating if the consistency of each unlabeled example is  
Figure 3: Time-periods of the academic year. beneficial for the current model per iteration. Thus, instead of examining the whole current \(L\) subset, only the neighbors of each \(x_{j}\in U\) are considered for measuring the corresponding consistency metric, which is described in Equation (1). As it is discussed in the original work of the COREG, by maximizing this variant--mentioned hereinafter as \(\delta_{x_{j}}\ \forall x_{j}\in U\)--we reach safely either to the maximization of the general consistency metric or we acquire a zero value. In the first case, we pick the \(j\)-th unlabeled instance with a greater impact. Otherwise, we do not select any of them.