Multinomial Random Forest: Toward Consistency and Privacy-Preservation
It addresses theoretical gaps in random forests for researchers, though it is incremental as it builds on existing RF methods with new theoretical guarantees.
The paper tackles the lack of theoretical understanding in random forests by proposing a multinomial random forest (MRF) that uses multinomial distributions for splits, proving its consistency and privacy-preservation, and showing it performs comparably to standard RF on multiple datasets.
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 the \emph{consistency} and \emph{privacy-preservation}. Instead of deterministic greedy split rule or with simple randomness, the MRF adopts two impurity-based multinomial distributions to randomly select a split feature and a split value respectively. Theoretically, we prove the consistency of the proposed 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.