# Hierarchical Modelling for CO\({}_{2}\) Variation Prediction for HVAC System Operation
## 2 Related Work  
The field of occupancy estimation through environmental data has incorporated ML and DL techniques. However, the research works differ regarding the features used for estimating the occupancy and the utility of the developed models in connection to HVAC systems. The work of [PERSON] et al. [26] is flagship research evaluating the usefulness of environmental sensors in capturing occupancy. A feature engineering module is employed to output the most relevant features out of lagged versions of CO\({}_{2}\) concentrations and acoustic levels. The authors report a 73% accuracy in occupancy estimation using Artificial Neural Networks, a Support Vector Machine, and Hidden Markov Models. The authors of [27; 28] employ low-complexity ML methods [29] such as Classification And Regression Trees (CART), and Random Forest (RF) for the approach in [27] and an Extreme Learning Machine Classifier for the approach in [28] to estimate occupancy. [PERSON] et al. [27] uniquely incorporate the time aspect in their feature engineering steps, whereas the methodology in [28] designs wrapper and filter methods to address the noisiness of the raw sensory data. Similarly, [PERSON] et al. [30] explored different combinations of lagged indoor environment data to predict CO\({}_{2}\) concentrations and made available the dataset used throughout their paper. To predict CO\({}_{2}\) in different future time horizons, the resultant features are fed to Ridge Regression (RR), Decision Trees (DT), RF, and Multi-Layer Perceptron (MLP) algorithms. Different types of Deep Neural Networks (DNNs) such as CNNs and Long Short-Term Memory (LSTM) were utilized for occupancy predictions. The work by [PERSON] et al. [24] combines CNNs and bi-directional LSTM to predict different classes of occupancy. The data in [31] incorporate HVAC sensory data with indoor climate sensory data to infer the number of occupants using particle filtering and neural networks. In a similar manner, [PERSON] et al. [23] tackle DCV by proactively predicting CO\({}_{2}\) concentrations. The authors of [32] uniquely tackle the transferability of occupancy estimation models using a transfer learning approach. To that end, the authors build their models using data collected in a small conference room. Later, the developed models are evaluated by transferring them to a large room. This process is achieved because of the layer-wise architecture of their developed CNN and LSTM models. Some of the literature identified the use of Wi-Fi signals to estimate occupancy. The authors of [18] collect the Channel State Information (CSI) from commercial Internet of Things (IoT) devices. A pipeline of DL models, encompassing Autoencoders and LSTM, is proposed to predict occupancy. Similarly, [PERSON] et al. [33] utilize Wi-Fi usage to predict occupancy trends using RF, DNNs, and LSTMs. Despite advancing the state-of-the-art in terms of occupancy estimation, there are some limitations to the current literature. A general limitation concerns the absence of publicly available datasets, hindering the comparison or replication of different approaches. The authors of [23; 30] broke this trend by relying on the same dataset that is used throughout the paper. In terms of the methodology, time dependencies are not incorporated in most previous works, which constitute a critical aspect in occupancy estimation and HVAC-related operations [34]. We compare our methodology with the applied methodology in [30], which is referred to as Feature Engineering for CO\({}_{2}\) Predictions (FECOP). The limitations of this work cover four main aspects:  
* Utility: Their work predicts CO\({}_{2}\) concentrations, such that a value of concentration can drastically vary from one spatial setting to another. For example, a specific prediction value can be interpreted differently in a room with two or 12 people. Mapping CO\({}_{2}\) concentrations to occupancy represents a physical modelling exercise, which varies depending on the studied space.