# Machine Learning Regressors to Estimate Continuous Oxygen Uptakees (\(\dot{VO}_{2}\))
## 2 Materials and Methods
### Modeling
XGBoost is an acclaimed ensemble learning technique utilized for both classification and regression tasks. It leverages multiple decision trees combined, exhibiting outstanding computational efficiency and speed compared to traditional gradient-boosting methods. Notable features include robust performance and speed, facilitated by parallel processing \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Participants** & **Age** & **Equation** \\ \hline \multirow{4}{*}{[PERSON] et al. (1985) [17]} & n = 100 & \multicolumn{2}{c}{Female: \(\dot{VO}_{2 max}\) (L.min\({}^{-1}\)) = \(-\)0.624 sex + 0.046 height \(-\) 0.021 age \(-\) 4.31} \\  & (50 M/50 & 15–71 & Male: \(\dot{V}_{2 max}\) (L.min\({}^{-1}\)) = \(-\)0.492 sex + 0.032 height \(-\) 0.024 age + 0.019 weight \(-\) 3.71} \\ \hline [PERSON] et al. (1984) [18] & n = 77 & 37–74 & Male: \(\dot{V}_{2 max}\) (mL.min\({}^{-1}\)) = weight \(\times\) (50.75 \(-\) 0.372 age) \\ \hline \multirow{4}{*}{[PERSON] et al. (1975) [16]} & n = 109 & \multicolumn{2}{c}{Female: \(\dot{V}_{2 max}\) (L.min\({}^{-1}\)) = 2.46 \(-\) 0.016 age} \\  & (109 F) & 10–68 & \(\dot{V}_{2 max}\) (mL.kg\({}^{-1}\).min\({}^{-1}\)) = 83.663 \(-\) 4.114 age + 0.127 age\({}^{2}\) \(-\) 0.0012 age \\ \cline{1-1}  & (109 F) & \(\dot{V}_{2 max}\) (mL.kg\({}^{-1}\).min\({}^{-1}\)) = 71.237 \(-\) 3.524 age + 0.104 age\({}^{2}\) \(-\) 0.0010 age \\ \cline{1-1}  & & \(\dot{V}_{2 max}\) (mL.kgLBM\({}^{-1}\).min\({}^{-1}\)) = 90.684 \(-\) 3.808 age + 0.118 age\({}^{2}\) \(-\) 0.0011 age \\ \cline{1-1}  & & \(\dot{V}_{2 max}\) (mL.kgLBM\({}^{-1}\).min\({}^{-1}\)) = 88.99 \(-\) 4.459 age + 0.140 age\({}^{2}\) \(-\) 0.0014 age \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 1: This flowchart shows the input parameters and the modeling approach. It was finalized to approach continuous \(VO_{2 max}\) estimation. for handling large datasets, automatic tree pruning to prevent overfitting, and strong regularization capabilities. Additionally, XGBoost (version 2.0.3) implements L1 (Lasso) and L2 (Ridge) regularization techniques to manage model complexity, enabling effective prevention of excessive tree depth and reduction of overfitting. Furthermore, it offers pruning functionality to manage model complexity and enhance generalization, along with automatic handling of missing data, distinguishing itself from algorithms requiring manual intervention. Before model training, missing data were addressed using XGBoost's built-in handling techniques, which automatically manage incomplete datasets. Additionally, anomalies detected in the data, such as extreme outliers, were filtered out using Z-score thresholds to ensure model reliability and accuracy. Lastly, the model provides flexibility by allowing custom optimization objectives and evaluation criteria, catering to diverse business needs and research questions. The model hyperparameters include a learning rate of 0.2. It allows the model to adapt its parameters during training. The maximum depth of each tree in the ensemble is set to 7, controlling the level of complexity. The model builds multiple trees to improve predictive accuracy with 220 estimators. The regularization parameters, L1 and L2 regularization, are set to 10 and 4, respectively, to prevent overfitting by penalizing coefficients. Other settings, such as random state, subsample, and verbosity, are also specified to ensure reproducibility, control sampling, and manage output verbosity during training. The code is available at [[https://github.com/SeanPresent/VO2](https://github.com/SeanPresent/VO2) max_Estimation]([https://github.com/SeanPresent/VO2](https://github.com/SeanPresent/VO2) max_Estimation), accessed on 25 August 2024.