# How to Open a Black Box Classifier for Tabular Data
## 3 Results
### Synthetic Data
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**AUC [CI]**} & **No. Input** & \multirow{2}{*}{**Training**} & **Optimisation** & **Performance** \\  & **Variables** & **(n = 6000)** & **(n = 2000)** & **Estimation (n = 2000)** \\ \hline \multirow{2}{*}{**Optimal classifier**} & **1** & **0.689 [0.675,0.702]** & **0.663 [0.639,0.687]** & **0.671 [0.648,0.695]** \\ MLP & 9 & 0.692 [0.678,0.705] & 0.665 [0.641,0.688] & 0.669 [0.646,0.693] \\ SVM & 9 & 0.708 [0.695,0.721] & 0.652 [0.628,0.676] & 0.660 [0.637,0.684] \\ GBM & 9 & 0.713 [0.700,0.726] & 0.586 [0.561,0.610] & 0.609 [0.584,0.633] \\ \hline \hline \multirow{2}{*}{**PRiSM models**} & \multirow{2}{*}{_Components_} & \multicolumn{3}{c}{_Dirac measure_} \\  & Lasso & 1 & 0.688 [0.675,0.701] & 0.663 [0.639,0.686] & 0.672 [0.648,0.695] \\ PRN & 1 & 0.690 [0.677,0.703] & 0.664 [0.640,0.687] & 0.670 [0.646,0.694] \\ PRN–Lasso & 1 & 0.688 [0.675,0.702] & 0.663 [0.639,0.686] & 0.672 [0.648,0.695] \\ prSVM & 14 & 0.691 [0.678,0.705] & 0.663 [0.640,0.687] & 0.671 [0.648,0.695] \\ prGBM & 1 & 0.687 [0.674,0.700] & 0.656 [0.633,0.680] & 0.661 [0.638,0.685] \\ \hline \hline \multirow{2}{*}{**PRiSM models**} & \multirow{2}{*}{_Components_} & \multicolumn{3}{c}{_Lebesgue measure_} \\ Lasso & 1 & 0.689 [0.676,0.702] & 0.664 [0.640,0.688] & 0.670 [0.647,0.694] \\ PRN & 1 & 0.690 [0.677,0.703] & 0.664 [0.640,0.687] & 0.670 [0.646,0.693] \\ PRN–Lasso & 1 & 0.690 [0.676,0.703] & 0.664 [0.641,0.688] & 0.670 [0.647,0.694] \\ prSVM & 7 & 0.690 [0.677,0.703] & 0.633 [0.640,0.687] & 0.672 [0.648,0.695] \\ prGBM & 1 & 0.688 [0.675,0.702] & 0.656 [0.632,0.680] & 0.659 [0.635,0.682] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Classification performance for the XOR function measured by the AUC [CI]. The inputs variables x\({}_{3}\) and x\({}_{4}\) are ideally selected solely for their bivariate response. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**AUC [CI]**} & **No. Input** & \multirow{2}{*}{**Training**} & **Optimisation** & **Performance** \\  & **Variables** & **(n = 6000)** & **(n = 2000)** & **Estimation (n = 2000)** \\ \hline \multirow{2}{*}{**Optimal classifier**} & **3** & **0.816 [0.802,0.830]** & **0.836 [0.813,0.860]** & **0.817 [0.793,0.841]** \\ MLP & 9 & 0.816 [0.803,0.830] & 0.833 [0.809,0.857] & 0.815 [0.791,0.839] \\ _SVM_ & 9 & _0.803 [0.790,0.817]_ & _0.797 [0.772,0.821]_ & _0.786 [0.762, 0.809]_ \\ GBM & 9 & 0.822 [0.810,0.834] & 0.826 [0.805,0.847] & 0.808 [0.787,0.830] \\ \hline \hline \multirow{2}{*}{**PRiSM models**} & \multirow{2}{*}{_Components_} & \multicolumn{3}{c}{_Dirac measure_} \\ Lasso & 3 & 0.815 [0.801,0.828] & 0.833 [0.809,0.857] & 0.813 [0.789,0.837] \\ PRN & 3 & 0.816 [0.802,0.829] & 0.835 [0.811,0.858] & 0.814 [0.790,0.838] \\ PRN–Lasso & 3 & 0.816 [0.802,0.830] & 0.835 [0.811,0.859] & 0.814 [0.791,0.838] \\ prSVM & 6 & 0.800 [0.787,0.813] & 0.813 [0.790,0.835] & 0.797 [0.74,0.820] \\ prGBM & 6 & 0.820 [0.807,0.832] & 0.828 [0.807,0.848] & 0.807 [0.786,0.829] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Classification performance for the logical AND function measured by the AUC [CI]. The input variables x\({}_{5}\) and x\({}_{6}\) are ideally selected with two univariate responses and a bivariate response.