## 3 Experiments
### Results and Discussion  
Based on the results of the experiment, it is also possible to build graphs of dependence on other parameters, for example, on the sample size, or plotting the stability of metric values, all other things being equal. Dependence is built by a piecewise line graph, and the area from the minimum to the maximum value of the metric is also painted over.  
As a result of the experiment with a given configuration, the values of the metrics were obtained. For example, the values of the faithfulness metric for the linear regression model are presented in Table 5.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Library Name** & **Description** & **Library Version** \\ \hline NumPy & \begin{tabular}{c} A library that implements linear algebra operations, \\ mathematical functions, elements of statistical analysis \\ \end{tabular} & 1.21.0 \\ \hline Matplotlib & Library for plotting various types of graphs & 3.5.1 \\ \hline \multirow{2}{*}{Scipy} & \begin{tabular}{c} Library designed to perform scientific and \\ engineering calculations \\ \end{tabular} & 1.8.0 \\ \hline Pandas & Library for working with tabular data structures & 1.4.1 \\ \hline \multirow{2}{*}{Shap} & \
\begin{tabular}{c} Library with implementation of the XAI \\ SHAP method \\ \end{tabular} & 0.40.0 \\ \hline \multirow{2}{*}{Lime} &
\begin{tabular}{c} Library with the implementation of the XAI \\ LIME method \\ \end{tabular} & 0.2.0.1 \\ \hline Scikit-learn & Library with tools for designing and training models & 1.0.2 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Table of used libraries.  
With correlation coefficients of 0.8 and especially 0.99, both methods show fairly significant errors. It is worth noting the rather high values of the metric for the non-linear marker generation function when applying methods to a linear regression model--methods are ways to identify non-linear dependencies and evaluate their contribution to model prediction.  
Graphs of dependences of the value of the monotonicity metric on the correlation coefficient are shown in Figure 5.  
It's worth noting that the XAI methods also need tweaking. For example, the stability and accuracy of the explanation of the Lime method can vary significantly with different kernel settings. The SHAP method has many modifications that differ in the way the Shapley values are calculated and taken into account. Additional studies are needed to study the effect of various parameters and method modifications.  
Depending on the other metrics, the incompleteness metric determines the correspondence of weights to prediction changes when noise is added to all features at once. The value of the metric itself is the average difference between these values, so the smaller the metric, the more complete the explanation can be considered. It can be seen from the graphs that with an increase in the correlation coefficient, the explanation becomes more complete. Higher values of the metric for binary tree models are also noticeable. In general, the values of the metric are low, which indicates the correct determination of the total contribution of all features to the model prediction.  
Figure 4: Dependence of the reliability metric on the correlation coefficient.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Marker Function**} & \multicolumn{6}{c}{**The Value of the Metric at the Correlation Coefficient**} \\ \cline{3-8}  & & **0.0** & **0.2** & **0.4** & **0.6** & **0.8** & **0.99** \\ \hline SHAP & Linear & 0.94 & 0.86 & 0.77 & 0.66 & 0.66 & 0.6 \\ \hline  & Non-linear & 0.96 & 0.87 & 0.81 & 0.81 & 0.76 & 0.62 \\ \hline LIME & Linear & 0.86 & 0.77 & 0.72 & 0.65 & 0.66 & 0.63 \\ \hline  & Non-linear & 0.92 & 0.88 & 0.8 & 0.8 & 0.72 & 0.57 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Confidence metric for a linear regression model.  
The results of calculating the incompleteness metric are shown in Figure 6.