## 1 Introduction
In particular, three substudies are implemented, each corresponding to the AD definition at different stages of the QSPR procedure, as described previously; namely, the stages of data preprocessing, model construction and model deployment. Therefore, in the first part of this study (referred to here as \"substudy\"), the AD definition is used as a data preprocessing method, in addition to the methods implemented in the first article, to remove outliers. At this stage, the number of descriptors is particularly high, with about 2500 descriptors. Several outlier detection methods are compared and the influence of the elimination of the identified outliers on the performance of the ML models is evaluated. All the types of outliers (i.e., X-outliers, y-outliers and Model-outliers) are considered. While y-outliers and Model-outliers are detected via boxplots (interquartile range method or IQR) and standardized residuals, respectively, X-outliers are identified on the basis of three simple methods having promising compatibility with high-dimensional problems. These methods are isolation forest (_iForest_), random forest-based confidence estimation (_RF confidence_) and k-nearest neighbors in a 2D projection of the descriptor space obtained via t-Distributed Stochastic Neighbor Embedding (_tSNE2D/kNN_). In the second substudy, the most appropriate AD definition method, as identified within the first substudy, is employed to visualize the location of the test data with respect to the AD defined by the training data. Finally, in the last substudy, the goal is to attempt a concrete deployment of the developed ML-QSPR model to new species, including the prediction and the analysis of the reliability of the predictions in terms of the AD, still based on the AD definition method identified in the first substudy. In the last two substudies, as they occur after dimensionality reduction, they rely on fewer descriptors, namely the 100 descriptors selected by means of a GA applied on the preprocessed data without outliers. Additionally, for these same substudies, further analyses are also provided regarding the potential sources of high prediction errors. Overview of the Methods for AD Definition/Outlier Detection in Descriptor-Space and Their Compatibility with High-Dimensional Data  
In this section, an overview of the methods for AD definition (or outlier detection) is provided, with a focus on X-outliers. The latter are effectively the most challenging to identify in view of their high dimensionality. First, the methods that are commonly employed to define the AD of QSPR/QSAR models are presented. These methods can be classified in different categories, including chemical-based methods, range-based methods, geometrical methods, distance-based methods and probability distribution-based methods, as illustrated in Figure 1. As these have already been exhaustively reported and described in several works [1; 16; 17; 18; 19], only a quick overview is provided here, for reasons of completeness, placing special emphasis on the low compatibility of these methods with high-dimensional data. Besides, they are generally applied during model construction or deployment. Inversely, other methods for outlier detection in high dimension, presented secondly here, including confidence estimation-based methods, subspace-based methods and other specific methods (e.g., _iForest_), are more suitable to the characteristics of the three substudies investigated in this work. Figure 1: Classical methods for AD definition: (**a**) chemical-based methods, (**b**) range-based and geometric methods, (**c**) distance-based methods/k-nearest neighbors, (**d**) probability distribution-based methods.