## 5 Conclusions and Perspectives  
In this work, the applicability domain (AD) of machine learning (ML) models trained on high-dimensional data is investigated. The considered models are two ML models developed in a previous article for the prediction of the ideal gas enthalpy of formation and entropy of molecules based on their high-dimensional descriptors [15]. The AD is crucial, as it describes the space of chemical characteristics in which the model can make predictions with a given reliability. This work studies the AD definition of a ML model all along its development procedure: during data preprocessing, model construction and model deployment. Inside each of these steps, the AD definition fulfills a different function. Three AD definition methods, commonly used for outlier detection in high-dimensional problems, were compared: isolation forest (_iForest_), random forest prediction confidence (_RF confidence_) and k-nearest neighbors in the 2D projection of descriptor space obtained via t-distributed stochastic neighbor embedding (_tSNE2D/kNN_). These methods compute an anomaly score which can be used similarly to the distance metrics of classical AD definition methods. A molecule is inside the AD if its distance to the training domain (or anomaly score here) is below a given threshold. Due to the curse of dimensionality, classical AD definition methods are generally unsuitable for high-dimensional problems. During data preprocessing, the three AD definition methods were used to identify outlier molecules and the effect of their removal was investigated. A more significant improvement in model performance could be observed when outliers identified with _RF confidence_ were removed (e.g., for a removal of 30% of outliers, test _MAE_ was divided by 2.5, 1.6 and 1.1 for _RF confidence_, _iForest_ and _tSNE2D/kNN_, respectively). While these three methods identify X-outliers, the effect of other types of outliers, namely Model-outliers and y-outliers, was also investigated. In particular, the elimination of X-outliers followed by elimination of Model-outliers enabled us to divide _MAE_ and _RMSE_ by two and three, respectively, while reducing overfitting phenomenon. The elimination of y-outliers did not display significant improvement in the model performance. During model construction, the AD serves to check how validation or test data are located in comparison with training data. All test data were close to training data according to the _RF confidence_ method; however, some test data displayed high prediction errors and tSNE 2D representations were used to identify the possible causes (e.g., molecule with chemical information not well represented in training data). Finally, the developed models were deployed to predict the thermodynamic properties of different categories of molecules. The results show that anomaly scores calculated using the _RF confidence_ method are not sufficient to judge the reliability of a prediction for a new molecule. Indeed, some new molecules with low/high anomaly scores were poorly/well predicted. Further research needs to be conducted to identify more appropriate metrics, possibly in combination with the _RF confidence_ method, to benefit from the information contained in each metric. More generally, the AD definition should be better integrated into any QSPR/QSAR procedure for later use of the developed models. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/a16120573/s1](https://www.mdpi.com/article/10.3390/a16120573/s1)]([https://www.mdpi.com/article/10.3390/a16120573/s1](https://www.mdpi.com/article/10.3390/a16120573/s1)), S1 (excel): Data, outliers and ML predictions. C.T. : literature review, conceptualization, methodology, data curation and modeling, writing (original draft preparation, review and editing). D.M. : supervision, methodology, writing (review and editing). S.L. and O.H. : data provision, molecular and thermodynamic analyses, generation of data for substudy 3, writing (review and editing).