# Machine Learning Regressors to Estimate Continuous Oxygen Uptakees (\(\dot{VO}_{2}\))
## 2 Materials and Methods
### Modeling  
Various regression models, including Extreme Gradient Boosting (XGBoost), Light Gradient Boosting Machine, Gradient Boosting Regressor, Linear Regression, and AdaBoost Regressor, are trained on the training set. The best-performing model is selected based on the Mean Absolute Percentage Error (MAPE) and further optimized via hyperparameter tuning. The tuned model's performance is evaluated using the test set. The accuracy of the model's predictions is assessed using the R-squared (\(R^{2}\)) metric that is computed to estimate the proportion of variance in the target variable \(VO_{2}\) (mL/kg/min) explained by the model. An important step in the preprocessing pipeline involves dividing \(\dot{V}O_{2}\) by weight (in kg) to normalize the \(VO_{2}\) values to observe standard ratings. This normalization enables fair comparisons across individuals of varying weights and allows the model to capture the relative oxygen consumption per unit of body mass. The features, including age, weight, height, HR, sex, and time, were selected based on their known physiological influence on oxygen consumption and performance in previous \(\dot{V}O_{2}\) estimation studies (Table 1). These variables are critical in capturing the variability in metabolic and cardiorespiratory responses during exercise. By obtaining \(\dot{V}O_{2}\) (mL/kg/min), representing oxygen consumption per kilogram of body weight per minute, the model's predictions are independent of body weight variations, enhancing interpretability and generalizability across diverse populations. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Participants** & **Age** & **Equation** \\ \hline \multirow{6}{*}{[PERSON] et al. (2013) [19]} & \multirow{6}{*}{n = 759 (394 M/365 F)} & \multirow{6}{*}{20–85} & Female: \(\dot{V}O_{2 max}\) (L.min\({}^{-1}\)) = 3.31 – 0.022 year \\  & & & \(\dot{V}O_{2 max}\) (mL.kg\({}^{-1}\).min\({}^{-1}\)) = 48.2 – 0.32 year \\ \cline{1-1}  & & & Male: \(\dot{V}O_{2 max}\) (L.min\({}^{-1}\)) = 4.97 – 0.033 year \\ \cline{1-1}  & & & \(\dot{V}O_{2 max}\) (mL.kg\({}^{-1}\).min\({}^{-1}\)) = 60.9 – 0.43 year \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Various \(\dot{V}O_{2 max}\) equations with participant numbers with age group. Various regression models were compared to assess performance. However, XGBoost was chosen based on the comprehensive comparison of metrics, such as MAE, MSE, RMSE, \(R^{2}\), RMSLE, MAPE, and training time in seconds [15]. Moreover, the various configurations operated to enrich model performance for the training process. The multicollinearity operated to eliminate highly correlated features. Additionally, 5-fold cross-validation was incorporated to assess the stability and generalization capability of the models (Figure 1). This method ensures that the model is robust and performs well on unseen data, helping to avoid overfitting and ensure that predictions generalize well to the broader population. Further, assigning a session ID ensured reproducibility of experiments, facilitating tracking and comparison of results. The tuned XGBoost model was optimized with a random search with the MAPE. It involves evaluating the model's performance on both training and testing datasets. Yet, predictions on the test data to estimate \(VO_{2}\) mL/kg/min values demonstrate the suitability of XGBoost as the most appropriate model for predicting \(VO_{2}\) mL/kg/min values. XGBoost has been widely used across different research domains, showcasing its versatility and effectiveness. Notable applications include predicting stock prices in financial markets [27], proactive damage estimation in infrastructure management [28], early earthquake magnitude prediction in earthquake research [29], forecasting air quality in environmental science [30], improving intrusion detection in cybersecurity [31], predicting treatment responsiveness in healthcare [32], and providing accurate forecasts of virus spread during the COVID-19 pandemic for public health management [33].