Algorithm 1:

Schematic overview of the proposed beta forest. During tree building, the algorithm applies the split rule introduced in Section 2.2.

Initialization: Fix num.trees, mtry and min.node.size.

Bootstrapping: Draw num.trees bootstrap samples from the original data.

Tree Building: For each of the num.trees bootstrap samples fit the tree-based beta regression model (as described in Section 2.2). More specifically, in each node of the trees,

– draw mtry candidate variables out of p variables,

– select the candidate variable and the split point that maximize the log-likelihood of the beta distribution and split the data into two children nodes,

– continue tree growing as long as the number of observations in each node is larger than min.node.size.

Prediction: For a new observation, drop the values of the explanatory variables down to the final nodes of the num.trees trees built in step ‘Tree Building’. Compute the ensemble estimate of the conditional mean by averaging the num.trees estimates of μ|X.