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

Data-driven multinomial random forest: A new random forest variant with strong consistency