Multinomial random forest

Despite the impressive performance of random forests (RF), its theoretical properties have not been thoroughly understood. In this paper, we propose a novel RF framework, dubbed multinomial random forest (MRF), to analyze its consistency and privacy-preservation. Instead of deterministic greedy split rule or with simple randomness, the MRF adopts two impurity-based multinomial distributions to randomly select a splitting feature and a splitting value, respectively. Theoretically, we prove the consistency of MRF and analyze its privacy-preservation within the framework of differential privacy. We also demonstrate with multiple datasets that its performance is on par with the standard RF. To the best of our knowledge, MRF is the first consistent RF variant that has comparable performance to the standard RF. The code is available at https://github.com/jiawangbai/Multinomial-Random-Forest.