. 2021 Mar 2;7:e374. doi: 10.7717/peerj-cs.374

Table 1. Algorithm for OBB predictor importance by permutation.

Algorithm: OBB Predictor Importance by Permutation
For tree t, t = 1……T Identify the OBB observations Identify The indices of the splitting predictor variables, $s_{t} \subseteq {1 \dots p} .$ Calculate the OBB error $ε_{t}$ . For each predictor variable $x_{j}, j \in s_{t}$ Randomly permute the observations of $x_{j}$ . Estimate the model error, $ε_{t j}$ using the OBB observations. Estimate the error difference $d_{t j} = ε_{t j} - ε_{t}$ At $d_{t j} = 0,$ the predictor variables are not split. For every predictor, calculate the mean, $- d_{j}$ and standard deviation, $σ_{j}$ of the error differences over the learners.The OBB predictor importance is given by $- d_{j} / σ_{j}$ for $x_{j}$ .

Algorithm: OBB Predictor Importance by Permutation

For tree t, t = 1……T

Identify the OBB observations
Identify The indices of the splitting predictor variables, $s_{t} \subseteq {1 \dots p} .$
Calculate the OBB error $ε_{t}$ .
For each predictor variable $x_{j}, j \in s_{t}$
- Randomly permute the observations of $x_{j}$ .
- Estimate the model error, $ε_{t j}$ using the OBB observations.
- Estimate the error difference $d_{t j} = ε_{t j} - ε_{t}$
- At $d_{t j} = 0,$ the predictor variables are not split.

For every predictor, calculate the mean,

- d_{j}

and standard deviation,

σ_{j}

of the error differences over the learners.The OBB predictor importance is given by

- d_{j} / σ_{j}

for

x_{j}