# Multinomial Random Forest: Toward Consistency and Privacy-Preservation

## TL;DR

This paper introduces a novel multinomial random forest (MRF) framework that achieves theoretical consistency and enhances privacy-preservation, while maintaining performance comparable to standard random forests.

## Contribution

The paper proposes the first consistent random forest variant, MRF, with theoretical guarantees and differential privacy analysis, advancing both the understanding and privacy aspects of RF.

## Key findings

- Proves the consistency of MRF.
- Demonstrates MRF's performance matches standard RF.
- Analyzes privacy-preservation within differential privacy framework.

## Abstract

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.