## 3 Results
### Variable Importance and Model Performance  
The estimation of the relative feature importance (Figure 6) shows that the model's prediction was highly influenced by the geometric mean computed on the other measurements (GM: 19.7%), which includes size, followed by the bizygomatic breadth (ZYB: 14.4%) and mastoid height (MDH: 10.2%). The remaining features had smaller contributions (each less than 10%), with the lowest scores shown by basion-bregma height and nasal height (BBH and NLH: 4.7%).  
Figure 4: Percentage distribution of the performance metrics—log loss and area under curve (AUC)—across all models trained and validated during parameter tuning. The dashed vertical lines indicate the performance of the best model selected (left: log loss; right: AUC).  
Figure 5: Learning curves showing performance of classification during the epochs. Performance is shown as log loss and area under curve (AUC), measured on the training and validation datasets (in darker and lighter colours, respectively). The similar pattern measured for the two datasets suggests that the performance learned through the training set was generalised to the validation set, thus indicating no overfitting occurred.  
When the performance was assessed on the 606 individuals (303 females, 303 males) of the test dataset, 266 out of 303 females were correctly sexed by the model, and 245 out of 303 for the male group. The model estimated sex with an accuracy of 0.843, and the intra-group accuracy was 0.809 for females and 0.878 for males, thus indicating a better performance for the male group. The log loss estimated on the test set performance was 0.348, much lower than the uninformative threshold of 0.693, suggesting that the observations are estimated with probabilities generally higher than 0.5. Figure 7 shows the histogram of the estimated probabilities of being female/male for the observations whose sex was correctly identified by the model. Ideally, we want the distribution to be negatively skewed (larger frequency of high probabilities); such a pattern was observed for our test sample, with 90% of the correctly sexed observations being estimated with a probability equal or higher than 0.66 (female) and 0.70 (male). The distribution of estimated probabilities for males was particularly skewed, with more than 40% of correctly sexed observations estimated with a probability equal or higher than 0.98.  
Figure 6: Relative importance of each feature in the best model selected. The importance is shown as a percentage. (GM: geometric mean; ZYB: bizygomatic breadth; MDH: mastoid height; AUB: biaurricular breadth; OBH: orbit height; GOL: glabella-occipital length; NLB: nasal breadth; OCC: lambda-opistion chord; OBB: orbit breadth; BBH: basion-bregma height; NLH: nasal height).  
Figure 7: Distribution of the probabilities returned by the best model for correctly estimated females (orange) and males (blue). The dashed vertical lines show the first decile of probability, which indicates the probability above which 90% of observations are estimated.  
The AUC of an ROC curve is a better estimator of performance than accuracy when we deal with binary classification. In fact, AUC provides an indication of the performance of both classes through a single metric. The ROC curve of the model prediction is shown in Figure 8. The AUC measured on the test set was 0.923.