# Hierarchical Modelling for CO\({}_{2}\) Variation Prediction for HVAC System Operation
## 5 Experimental Setup
### Evaluation Metrics  
The HMCOVP is evaluated against FECOP [30] and 1D CNNs, a popular method for time-series prediction. Since the problem of predicting CO2 variation prediction is a regression task, multiple evaluation metrics such as Mean Square Error (MSE) or Mean Absolute Error (MAE) can be used. Choosing one of these metrics depends on the experiments' main goals.  
The MSE metric emphasises the large errors while minimizing the effect of the smaller ones. On the other hand, the MAE equalises the effect of all individual errors. No anomaly detection method was applied to sanitize the gathered data, which suggests the existence of data corrupted with noise. This noise originates either from the environment itself or from the inaccuracies of the sensing technologies. Such circumstances call for a robust evaluation metric that can offset the noise's effect. On a different note, the small prediction errors that are continually produced by models can result in long-term consequences to the HVAC systems. The predictions of CO2 variations affect the ventilation systems that need to maintain the indoor CO2 concentrations within acceptable levels and the estimation of current occupancy changes dictating the HVAC system's operation. Consequently, small deviations, while insignificant in the short term, can accumulate unnecessary activation of HVAC systems, increasing the building's Carbon footprint and energy expenditure. Large deviations of predictions originate either from models' under-fitting data, which can be identified if it is a shared trend among different input values or from the existence of anomalous data that the model fails to fit. The anomalous data can be manifested by wrong sensor readings, corrupting the data with noise, or the occurrence of rare events that have little implications on long-term energy expenditure. As such, the robustness requirement and the equal importance of small and large deviations favour the use of MAE as an evaluation metric.  
The MAE evaluation metric is used to find the best set of hyper-parameters on the validation set and to compare the performance of the HMCOVP, FECOP, and 1D CNNs on the testing set. The methods are evaluated on a set of CO\({}_{2}\) variations exceeding pre-defined thresholds, including \(\{5,10,20,40,50,75,100\}\). These thresholds unveil different methods' capability to predict big variations in CO\({}_{2}\) concentration, which can potentially activate the HVAC systems and determine the instantaneous energy expenditure. The average MAE combining all these thresholds is employed to highlight the performance differences between the proposed methodology and the other approaches, providing a comprehensive overview of the proposed methods' performance under different circumstances. The training and instance-wise testing times are incorporated into the evaluation to gauge the methods' ability to learn in resource-constrained environments. Different CO\({}_{2}\) variation thresholds and execution times are important factors of the deployment of proper solutions for building operators. The accurate predictions of CO\({}_{2}\) changes are envisioned to facilitate the ventilation system's decision-making processes. Therefore, the reduction in the superfluous activation of these systems translates into limiting energy expenditure. In the grand scheme of things, this methodology contributes to the mitigation of Carbon emissions, which can be quantified depending on the ore used for electricity production.