than deep neural networks in terms of data and computa-
tion, and our experiments suggest that ARF convergence is
usually fast even for δ = 0 (see Sect. 5).
With our ARF in hand, the algorithm proceeds as follows.
For each tree b, we record the split criteria θ(cid:96)
b and empirical
b) of each leaf (cid:96). Call these the leaf parame-
coverage q(θ(cid:96)
ters. Then we estimate distribution parameters ψ(cid:96)
b,j inde-
pendently for each (original) Xj within X (cid:96)
b , e.g. the kernel
bandwidth for KDE or class probabilities for MLE with
categorical data. In the continuous case, ψ(cid:96)
b,j must either
encode leaf bounds (e.g., via a truncated normal distribution
with extrema given by θ(cid:96)
b) or include a normalization con-
stant to ensure integration to unity. The generative model
then follows a simple two-step procedure. First, sample a
tree uniformly from [B] and a leaf from that tree with proba-
bility q(θ(cid:96)
b), just as we do to construct synthetic data within
Adversarial Random Forests for Density Estimation and Generative Modeling