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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 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 split feature and a split value respectively. Theoretically, we prove thearXiv:1903.04003v3 fatcat:tzlzd2j575hznc2owyn7vadxm4