latter, we ﬁx ntrn = 2000. We ﬁnd that PWC methods
fare poorly, with much greater NLL in all settings. This
is likely due to the unrealistic uniformity assumption, ac-
cording to which the corner of a hyperrectangle is no less
probable than the center. GeFs, which also use a Gaussian
mixture model to estimate densities, perform better in this
experiment. However, FORDE dominates throughout.
Panel (B) clearly illustrates that unsupervised methods are
unaffected by changes in signal sparsity, since their splits
are independent of the outcome variable Y . By contrast,
Adversarial Random Forests for Density Estimation and Generative Modeling