Algorithm 3 FADEL Ensemble Learning-based Prediction

Input: Test sample $x_{\ast }$; trained base models ${\left\{{\mathcal{H}}_m\right\}}_{m=1}^4$; Random Forest meta-model RF with T trees Output: Final prediction $\widehat{y}\left(x_{\ast }\right)$ 1.  Initialize probability vector v of length 4 2.  For $m=1$ to 4: 3.      Compute raw score: $s_m\leftarrow {\mathcal{H}}_m\left(x_{\ast }\right)$ 4.          Compute probability: $p_m\leftarrow \sigma \left(s_m\right)={\displaystyle \frac{1}{1+\exp (-s_m)}}$ 5.      $v\left[m\right]\leftarrow p_m$ 6.  Initialize predictions array ${\left\{{\widehat{y}}_t\right\}}_{t=1}^T$ 7.  For $t=1$ to T: 8.      Identify leaf region $R_{t,j}$ containing v 9.          Retrieve probability vector: $q_{t,j}$ 10.        Compute prediction: ${\widehat{y}}_t\left(x_{\ast }\right)=\arg {\max }_{c\in \mathcal{Y}}{q}_{t,j}(y=c)$ 11.     ${\widehat{y}}_t\left[t\right]\leftarrow {\widehat{y}}_t^{(\ast )}$ 12.   Aggregate final prediction by majority voting: $\widehat{y}(\ast )=\mathrm{mode}\left\{{\widehat{y}}_1^{(\ast )},{\widehat{y}}_2^{(\ast )},\dots ,{\widehat{y}}_T^{(\ast )}\right\}$ 13.   return  $\widehat{y}\left(x_{\ast }\right)$