  In this paper, we modify the proof methods of some previously weakly
consistent variants of random forests into strongly consistent proof methods,
and improve the data utilization of these variants in order to obtain better
theoretical properties and experimental performance. In addition, we propose a
data-driven multinomial random forest (DMRF), which has the same complexity
with BreimanRF (proposed by Breiman) while satisfying strong consistency with
probability 1. It has better performance in classification and regression
problems than previous RF variants that only satisfy weak consistency, and in
most cases even surpasses BreimanRF in classification tasks. To the best of our
knowledge, DMRF is currently a low-complexity and high-performing variation of
random forests that achieves strong consistency with probability 1.
