Source Code of Machine Learning Algorithm

Machine learning was used to model associations between exercise performance and metabolite responses. Model variables included metabolite response to exercise expressed as log2([post-exercise]/[pre-exercise]) (independent variable), VO2max, and RQ. Due to small sample size, samples were randomly sampled without replacement for 5 unique training and testing sets of combined RT and CT (80/20 split). Gradient boosting regression tree (GBRT) was used for machine learning analyses (https://scikit-learn.org/stable/modules/ensemble.html#gradient-tree-boosting). For each training/testing set split, the lambda parameter was tuned based on the training set only using 10-fold cross-validation. All correlation analyses with model predictions are based on testing set predicted values. Predictive performance was evaluated based on the Pearson correlation coefficient between the predicted values and actual values. The SHAP (SHapley Additive exPlanations) feature values provided multiple explanation for the models, and were calculated to evaluate the interpretation of top 20 metabolites contributed significantly to the predicted models. The Force plot algorithm was used to calculate the coefficients of potential markable contributors to predict VO2max or RQ. All these calculations and analyses were performed in Python using Scikit-learn database (https://scikit-learn.org).