Algorithm 2.

Exchangeably Weighted Regression Ensembles

1: Generate M independent sets of exchangeable bootstrap weights ω1,... ,ωn.

2: For each set of bootstrap weights, build a fully grown CART tree using Step 1 of Algorithm 1 with the loss function ${\sum }_{i\in \mathrm{node}}{\omega }_{i}L(Z_i,\psi (W_i))$ where, at each stage of splitting, mtry covariates are randomly selected from the p available covariates for candidate splits.

3: For each tree in the forest, calculate an estimator at each terminal node and average over the results obtained for the M sets of bootstrap weights to get the final ensemble predictor.