## 1 Introduction
To improve its accuracy, we jointly optimize both parameters and structure of the BRBES with the Joint Optimization of Parameter and Structure (JOPS) algorithm [49]. With this joint optimization using supervised labeled data, the initial BRBES transitions to the supervised BRBES. We continue to optimize this supervised BRBES until the confidence level of its accuracy reaches a certain threshold. After reaching this accuracy threshold, the supervised BRBES transitions to the \"confident BRBES\". We then integrate SSL with this confident BRBES to train it with a larger synthetic dataset. For the SSL method, we employ the self-training model [50] in this research. As part of the self-training model, we perform data augmentation to synthetically create new unlabeled data through transformation of the existing labeled data points [51]. Through data augmentation, we add more training examples of energy consumption to address overfitting and poor generalization [52]. In this study, we employ two types of data augmentation: \"weak\" and \"strong\". Weak augmentation involves mild transformation of the original data points within a predefined range to increase data variability and generalization. On the other hand, strong augmentation involves more complex transformation to create challenging training examples that force the prediction model to learn more robust features. First, we apply weak augmentation to synthetically generate new unlabeled energy consumption data with equal distribution within a predefined range for each antecedent attribute of BRBES. Thus, we ensure proper diversity and density of the unlabeled data, resulting in a balanced unlabeled energy dataset. We then employ the confident BRBES to assign pseudo-labels to the weakly augmented unlabeled data. Thus, with the self-training model, we ensure that the pseudo-labels are assigned by no model other than the BRBES. This makes the pseudo-labels representative of domain knowledge while handling associated data uncertainties. We then optimize the confident BRBES with both a labeled and a weakly augmented pseudo-labeled energy dataset. If the accuracy increases, the confident BRBES will transition to the \"weakly semi-supervised BRBES\". We then apply strong augmentation to generate more complex unlabeled energy data. To assign pseudo-labels to these strongly augmented unlabeled data, we apply the weakly semi-supervised BRBES. We then optimize this weakly semi-supervised BRBES with labeled as well as weakly and strongly augmented pseudo-labeled energy data. If the accuracy increases through this optimization, the weakly semi-supervised BRBES will transition to \"semi-supervised BRBES\". Thus, with this semi-supervised BRBES, we provide energy consumption prediction with improved accuracy by overcoming the scarcity and imbalance of supervised labeled data. After obtaining predictive energy consumption output with this semi-supervised BRBES, we provide an explanation and counterfactual of this output to the end user through a user interface. The explanation and counterfactual are prepared in nontechnical human language so that any layperson can understand them. The explanation and counterfactual, formulated based on domain knowledge, create a relationship of trust between our model and human user [37]. Thus, we propose a semi-supervised explainable BRBES framework to predict the continuous value of the energy consumption of buildings accurately in units of kilowatt-hour (kWh) despite the scarcity of labeled data while providing an explanation and counterfactual based on knowledge of energy consumption domain. Thus, we perform semi-supervised regression while also explaining the regression output. We evaluate the accuracy, explainability, and counterfactual of our proposed semi-supervised framework with relevant metrics. In terms of accuracy, our proposed framework outperforms the supervised BRBES through semi-supervised learning.