## 5 Proposed Semi-Supervised Regression Wrapper Scheme
This strategy is similar to fitting an instance-based algorithm, like the k-Nearest Neighbors (kNN) [51], for selecting the unlabeled instances to augment the current labeled set per iteration, as it was preferred during the COREG approach. However, this fact does not hinder us from applying different kinds of regressors on the augmented labeled set, thus exploiting possible advantages of other learning models for capturing better the underlying relationships of the examined data. Based on our search in the literature, such a study has not yet been done. Moreover, the already mentioned augmented per iteration labeled subset does not contain exclusively accurate values of the target attribute per its included instance, since during the training stage pseudo-labeled instances are joining the initially labeled examples, and their estimated values may differ from the actual one. This kind of noise into any SSL scheme may heavily deteriorate their total performance, settling them as myopic approaches that cannot guarantee safe predictions and violate the interpretation of the exported results. Therefore, to alleviate the inherent confidence of COREG, we examine its efficacy on an EDM task that supports the multi-view description, increasing, thus the diversity of the trained regressors. Since the COREG algorithms is based on the co-training scheme, the feature space \(F\) of the original problem \(D\) is split into two disjoint views: \(F=F_{1}\cup F_{2}\). Although the random split has been proven quite competitive in several cases [52; 53], co-training scheme should work if these two views are independent and sufficient. The examined real-world problem brings a multidimensional and multi-view description that encourages us to train each regressor on separate views and get trustworthy predictions that would not harm our learning model regarding neither its predictiveness nor its interpretability despite the limited labeled data. Algorithm 1 presents the pseudocode of the end-to-end SSR pipeline. ```
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* Initially collected labeled \(\mathbf{L}=[x_{i},\ \psi_{i}]_{i=1}^{i}\) and unlabeled \(\mathbf{U}=[x]_{i=1}^{i}\), instances, where \(\mathbf{D}=\mathbf{L}\cup\mathbf{U}\) and \(\mathbf{L}\cap\mathbf{U}=\varnothing\)
* \(F_{1},F_{2}\): provide the split of the original feature space \(F\), where \(F=F_{1}\cup F_{2}\) and \(F_{1}\cap F_{2}=\varnothing\)
* Define Max_iter: maximum number of semi-supervised iterations and \(f\): performance metric
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* Set iter = 1, consistentSet = \(\emptyset\)
* Train selector1, regressor on \(\mathbf{L}(F_{i})\ \forall i\in\{1,2\}\)
* While iter \(\preceq\) Max, iter do
* For each \(i\in\{1,2\}\) do
* For each \(x_{j}\in\mathbf{U}\) do
* Compute \(\delta_{x_{j}}(f)\) based on selector1\(\forall i\in[1,2]\)
* If \(\delta_{x_{j}}(f)>0\) : add j to consistentSet
* If consistentSet is empty do
* iter:= iter + 1 and continue to the next iteration
* else do
* Find the index \(\gamma\) of consistentSet s.t. \(\gamma^{\prime}=arg\ \max\delta_{x_{j}}\)
* Update \(\mathbf{U}:\ \mathbf{U}\ \leftarrow\ \mathbf{U}-\left\{\gamma_{\gamma}\right\}\)
* For \(i\in\{1,2\}\) do Update \(\mathbf{L}:\ \mathbf{L}\ \leftarrow\ \mathbf{L}\cup\left\{\gamma_{\gamma^{\prime}}\right\}\), regressor \(\sim i\left(x_{\gamma^{\prime}}\right)\)], where \(\
eg\)i means the opposite index of the current
* Retrain selector1, regressor on \(\mathbf{L}(F_{i})\forall i\in\{1,2\}\)
* iter:= iter + 1
* Apply the next rule to each met \(x_{\textit{test}}\) instance: \[h_{\textit{COREG}}(x_{\textit{test}})=\
icefrac{{1}}{{2}}\cdot(\textit{ regressor1}(x_{\textit{test}})+\textit{regressor2}(x_{\textit{test}}))\]
```  
**Algorithm 1**The extended framework of the COREG algorithm.