Algorithm 1: The RF Algorithm

1: $\mathfrak{D}=\left\{\left(x_1,y_1\right),\dots ,\left(x_N,y_N\right)\right\}$ defines the training data with $x_i={\left(x_{i,1},\dots ,x_{i,p}\right)}^T.$

2: For $j=1$ to $J$.

3: Take a bootstrap sample ${\mathfrak{D}}_j$ of size $N$ from $\mathfrak{D}$.

4: Fit a tree using ${\mathfrak{D}}_j$ and binary recursive partitioning.

5: Begin with all observations in a single node.

6: Repeat for every unsplit node.

7: Select $m$ predictors in a random manner from $p$.

8: Find the optimal binary split on the $m$ predictors.

9: Apply the split.

10: Until stopping criteria are met.

11: To predict a new point x, use.

$\widehat{f}\left(x\right)=\arg ma{x}_y{{\displaystyle \sum }}_{j=1}^{J}I\left(\widehat{h_j}\left(x\right)=y\right)$ where $\widehat{h_j}\left(x\right)$.

corresponds to the prediction of the response variable at $x$ using the $j^{th}$ tree.