## 4 Discussion  
The Ridge classifier used a weighted combination of the extracted features, allowing a ranking of them in relation to their importance in the prediction. The re-iteration of the proposed pipeline for 200 different cross-validations confirms the robustness of the model and the extracted features for the prediction. The robustness of the extracted features was confirmed also by the possibility to use the entire set of PLR signals belonging to the ON population. Thus, our results support the hypothesis of a bilateral alteration of the pupillary response in the ON population compared to healthy subjects [27]. This result could be explained by different theories. One possible explanation could be the alteration of the pupillary response in both eyes is secondary to a previous or concomitant sub-clinical episode of ON in the contralateral eye, supporting the role of pupillometry as a diagnostic tool in detecting inapparent signs of optic nerve inflammation. However, another explanation could be that patients with unilateral ON might present an alteration of the pupillary response in the contralateral eye, in the absence of an inflammation of the optic nerve, secondary to a reduced afferent stimulus, and a subsequently reduced activation of the efferent pathway. Moreover, because of the strict connection between ON and MS, some of the patients could be in an early stage of the MS pathology, undergoing neurological degeneration in both eyes. The most informative feature for the classification (20% of mean importance) is the baseline diameter in the first isotopic region. The \(D_{0}\) feature is simple and easy to acquire since it does not necessarily need a light stimulus. It was already considered in a previous study on Multiple Sclerosis, where ON is the first inflammatory event in 15-20% of patients (ref. [PERSON] et al. [29]). Multiple Sclerosis patients tend to have smaller baseline values, and then smaller pupil diameter in rest dark conditions, which confirmed, even if with different techniques, the essence of the result of [PERSON] et al. [29]. This feature measures a balance between the parasympathetic and the sympathetic function [19]. The second most important feature (mean of 17% importance) is the global area under the PLR signal. The A\({}_{\text{tot}}\) feature was designed to capture the overall behavior of the PLR signal, regardless of the scotopic/photopic subdivisions. This result highlights the coexistence of multiple factors in the PLR signal capable of providing information on the classification of ON vs. Healthy patients and the complexity of their interconnections. Indeed, it suggests that the afferent signal is affected in ON, with a subsequent alteration in both the parasympathetic and sympathetic function in a non-trivial way, not easily detectable with previously measured features, such as maximum contraction velocity  
Figure 2: Results obtained by the proposed machine learning pipeline for the automated classification of ON vs. Healthy patients analyzing the set of features extracted from the PLR signals. (**a**) Distribution of the accuracy scores and mean \(\pm\) standard deviation, achieved by the proposed pipeline on 200 different 5-fold cross-validations procedures. (**b**) Distribution of the Matthews Correlation Coefficient scores and mean \(\pm\) standard deviation, achieved by the proposed pipeline on 200 different 5-fold cross-validations procedures. (**c**) Ranking of the top-performing features identified by the Ridge classifier. The feature importance was assessed by computing the loss of accuracy when permutating each variable. Bars are the 95% confidence intervals of 5000 bootstrap resamples from 500 different random permutations. (\(max\{v_{contraction}\}\)), minimum relative amplitude (\(min\{D\}\)) for the parasympathetic ones, and maximal re-dilation velocity (\(max\{v_{dilation}\}\)) and a generic re-dilation time (\(\lambda_{t}\)) for the sympathetic ones.