## 2 Materials and Methods
### Predictive Models  
The learning models considered in this study are the following:  
* _K_-Nearest Neighbours (KNN)
* Linear Discriminant Analysis (LDA)[25; 26].
* Logistic regression (logit)
* Ridge classifier (Ridge)
* Gaussian Naive Bayes classifier (GNB) [27; 28].
* Classification tree (tree) [29].
* Random forest (forest) [30].
* Support Vector Machine (SVM) [31].
* Multi-Layer Perceptron (MLP) [32; 33; 34].
* eXtreme Gradient Boosting (XGB)  
KNN classifiers are very simple to compute but have the main drawbacks of involving high computation times for large data-sets and to be hard to interpret since in distances computation between examples, no explicit feature selection or weighting can be directly computed. Classification trees are basic classifiers which can be used in non-linear contexts. They are often used for their graphical outputs which are easily interpretable and provide visualisation of multi-dimensional features impact on class variables. In our context, such tools could help experts to gain knowledge about the relation between training loads and injury risk. They were compared to different generalised linear classifiers which are usually categorized as generative or discriminative models [35]. Naive Bayes classifier and LDA were used as standard generative models, logit, Ridge, MLP and SVM as  
\begin{table}
\begin{tabular}{c l l} \hline \hline accuracy & \(\frac{TP+TN}{TP+FP+TN+FN}\) & How many examples \\  & & we correctly predicted \\ \hline precision & \(\frac{TP}{TP+FP}\) & How many of those \\  & & predicted injury are actually injury \\ \hline recall & \(\frac{TP}{TP+FN}\) & Of all injury examples, \\  & & how many of those we correctly predicted \\ \hline Area Under the _ROC_ Curve (_AUC_) & _ROC_ = rate (TP/FP) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Binary measures of predictive performance.  
discriminative ones. In [PERSON] et al. (2020), the authors found that classification tree had higher predictive performance than other models (including random forest), but since ensemble models are usually more accurate than simple trees, forest and XGB models were also included in this study. Moreover, all tree-based classifiers (tree, forest and XGB) provide features weights which are precious in terms of models interpretation.  
Different sets of attributes (see Table 3) were considered in order to highlight the potential predictability of injuries levels. First, only the number of past injuries was used as predictor of future injury, then personal features (age, height, weight and \(BMI\)) were added to the learning data. The \(GPS\) and questionnaire data were first separately considered (in addition to past injuries and personal features) and finally the largest set of variables included all together the different input variables (see Table 1).  
All models were compared to a _baseline approach_ (B) which consists in predicting systematically the most frequent class (e.g., if there is 75% no injury and 25% injury, inNode will systematically predict no injury).  
All experiments were performed on Python with the following libraries: pandas, xgboost, xgboost, matplotlib, IPython, polydtplus and performance results were plotted with the _ggplot2_ package of R.