## 4 Evaluation Models
### Glass Box ML Models  
We introduce the following three glass Bbox ML models in our study: GAM, GNAM, and EBM. (1) GAM (generalized additive model)  
GAMs are a semi-parametric extension of the generalized linear models that allow for nonparametric fittings of complex dependencies of response variables. A GAM adopts a sum of arbitrary functions of variables (possibly nonlinear) that represent different features via splines, which altogether describe the magnitude and variability of the response variables [30]. For a univariate response variable of multiple features, GAM is expressed by Equation (9):  
\[g(E[y])=\beta_{0}+\sum f_{j}\left(x_{j}\right)+\varepsilon \tag{9}\]  
where \(\beta_{0}\) is the intercept parameter, \(x_{j}\) represents independent variables, \(y\) is the dependent variable, \(g(0)\) is the link function that relates the independent variables to the expected value of the dependent variable, and \(\varepsilon\sim N\left(0,\delta^{2}\right)\) represents a random variable [31]. GAMs are interpretable by design because of their functional forms that make it easy to reason about the contribution of each feature to the prediction. The analysis of the data in our study based on GAM is performed by using the pyGAM module with the source code available at [[https://github.com/dswah/pyGAM/tree/master](https://github.com/dswah/pyGAM/tree/master)]([https://github.com/dswah/pyGAM/tree/master](https://github.com/dswah/pyGAM/tree/master)) (accessed on 20 February 2025). The model's hyper-parameters are not optimized by us and are set to default values. (2) GNAM (generalized neural additive model)  
GNAMs [32] are a neural network-based extension of GAMs through replacing the mathematical exploration of \(f_{j}\left(x_{j}\right)\) in Equation (9) by MLPs. The GNAM can be expressed by the following:  
\[g(E[y])=\beta_{0}+\sum f_{j}^{MLP}\left(x_{j}\right)+\varepsilon \tag{10}\]  
where \(f_{j}^{MLP}\left(x_{j}\right)\) is the jth MLP network. The architecture of the GNAM with \(k\) input explanatory variables and presuming just one hidden layer and \(a\) as a corresponding activation function is presented in Figure 5.  
The analysis of the data in our study based on GNAM is performed by using the NAMpy package with the source code available at [[https://github.com/AnFreTh/NAMPy/tree/main](https://github.com/AnFreTh/NAMPy/tree/main)]([https://github.com/AnFreTh/NAMPy/tree/main](https://github.com/AnFreTh/NAMPy/tree/main)) (accessed on 20 February 2025). The MLP's hyper-parameters are not optimized by us and are set to default values. Figure 5: The architecture of the GNAMs with \(k\) input explanatory variables and presuming just one hidden layer. (3) EBM (explainable boosting machine)  
The basic idea behind EBM is similar to GAM and GNAM. However, EBMs offer a few major improvements over the traditional GAMs family [33]. First, EBMs learn each feature function \(f_{j}\) using gradient-boosted ensembles of bagged trees. Similar to gradient-boosted tree models, EBMs\({}^{\prime}\) training comprises a large number of trees in a sequential manner, each explaining the errors of the previous one. Though, in contrast, in EBM, each tree is built based on a single input feature. It first builds a small tree with the input feature \(x_{1}\) and computes the residuals (\(\varepsilon\)). It then fits the second tree with a different input feature \(x_{2}\) to the residuals and goes on through all input features to complete the ongoing iteration. To mitigate the effect of each input feature's order in the sequence, EBM incorporates a small learning rate. Moreover, sequentially estimating each feature one-at-a-time in a round-robin fashion mitigates potential collinearity issues between predictors [34]. Once the first iteration is complete, the training is reiterated for a large number of iterations to ensure an acceptable accuracy.