A random forest (RF) is a bootstrap-aggregated (bagged) en-
semble of independently randomized trees (Breiman, 2001),
typically built using the greedy classiﬁcation and regres-
sion tree (CART) algorithm (Breiman et al., 1984). RFs
are extremely popular and effective, widely used in areas
like bioinformatics (Chen and Ishwaran, 2012), remote sens-
ing (Belgiu and Dr˘agu¸t, 2016), and ecology (Cutler et al.,
2007), as well as more generic prediction tasks (Fernández-
Delgado et al., 2014). Advantages include their efﬁciency
(RFs are embarrassingly parallelizable), ease of use (they re-
quire minimal tuning), and ability to adapt to sparse signals
(uninformative features are rarely selected for splits).
It is well-known that tree-based models can approximate
joint distributions. Several authors advocate using leaf
nodes of CART trees as piecewise constant density esti-
mators (Ram and Gray, 2011; Wu et al., 2014; Wen and
Hang, 2022). While this method provably converges on
Adversarial Random Forests for Density Estimation and Generative Modeling