Algorithm 3: Random Forest

Input: H and an RF training dataset: number of replicates and threshold. Output: $Y_s$ and $Y_{\phi }$     Let ${\mathfrak{s}}_Y=\left\{\frac{H}{X}\right\},M=\left|\right|{\mathfrak{s}}_Y\left|\right|$     For r$\leftarrow 1$ to R do         ${\mathfrak{s}}_{\mathfrak{v}}\leftarrow permute\left({\mathfrak{s}}_Y\right)$         ${\mathfrak{s}}_{Y\mathfrak{v}}={\mathfrak{s}}_Y\cup {\mathfrak{s}}_{\mathfrak{v}}$        Build RF model from ${\mathfrak{s}}_{Y\mathfrak{v}}$ to produce $\left\{{\omega }_{Y_i}^{\gamma }\right\}$        $\left\{{\omega }_{{\mathfrak{v}}_i}^{\gamma }\right\}$ and ${\omega }_{\mathfrak{v}}^{max},\left(i=1,\dots ,M\right).$    Set $\tilde{Y}=\theta$    For i $\leftarrow 1$ to M do         Compute the Wilcoxon rank- sum test with ${\omega }_{Y_i}$ and ${\omega }_{\mathfrak{v}}^{max}$         Compute $p_i$ values for each feature $Y_i$        if $p_i\le \theta$ then             $\tilde{Y}-\tilde{Y}\cup Y_i\left(Y_i\in {\mathfrak{s}}_Y\right)$    Set $Y_{\mathfrak{s}}=\theta ,Y_w=\theta$    Compute $Y^2\left(\widetilde{Y,}X\right)$ statistic to get $p_i$ value    for i$\leftarrow 1$ to $\left|\right|\tilde{Y}\left|\right|$ do       if $(p_i<0.05)$ then             $Y_{\mathfrak{s}}=Y_{\mathfrak{s}}\cup Y_i\left(Y_i\in \tilde{Y}\right)$    $Y_w=\{\tilde{Y}\backslash Y_{\mathfrak{s}}\}$     Return    $Y_{\mathfrak{s}},Y_w$