  In this article, we strengthen 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, based on the
multinomial random forest (MRF) and Bernoulli random forest (BRF), we propose a
data-driven multinomial random forest (DMRF) algorithm, which has lower
complexity than MRF and higher complexity than BRF while satisfying strong
consistency. It has better performance in classification and regression
problems than previous RF variants that only satisfy weak consistency, and in
most cases even surpasses standard random forest. To the best of our knowledge,
DMRF is currently the most excellent strongly consistent RF variant with low
algorithm complexity
