ARFs enable fast, accurate density estimation and data syn-
thesis. However, the method is not without its limitations.
First, it is not tailored to structured data such as images or
text, for which deep learning models have proven especially
effective. See Appx. B.5 for a comparison to state-of-the-art
models on the MNIST dataset, where convolutional GANs
clearly outperform FORGE, as expected. Where our method
excels, by contrast, is in speed and ﬂexibility.
We caution that our convergence guarantees have no impli-
cations for ﬁnite sample performance. Though ARFs only
required one or two rounds of training in most of our ex-
periments, it is entirely possible that discriminator accuracy
increase from one round to the next, or that Alg. 1 fail to
terminate altogether for some datasets. (In practice, this
behavior is mitigated by increasing δ or setting some max-
imum number of iterations.) For instance, on MNIST, we
generally ﬁnd accuracy plateauing around 65% after ﬁve
Adversarial Random Forests for Density Estimation and Generative Modeling