# Inference with Mondrian Random Forests

arXiv: https://arxiv.org/abs/2310.09702 · HTML: https://mlsanity.com/paper/2310.09702/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 38 references that are in the map.
- First posted on arXiv 15 Oct 2023.

## Builds on (most cited first, 10 of 10)

- [Consistency of random forests](https://mlsanity.com/paper/1405.2881/) (2014)
- [Deep Forest](https://mlsanity.com/paper/1702.08835/) (2017)
- [Large Scale Prediction with Decision Trees](https://mlsanity.com/paper/2104.13881/) (2021)
- [Mondrian Forests: Efficient Online Random Forests](https://mlsanity.com/paper/1406.2673/) (2014)
- [Local Linear Forests](https://mlsanity.com/paper/1807.11408/) (2018)
- [Minimax optimal rates for Mondrian trees and forests](https://mlsanity.com/paper/1803.05784/) (2018)
- [AMF: Aggregated Mondrian Forests for Online Learning](https://mlsanity.com/paper/1906.10529/) (2019)
- [Stochastic geometry to generalize the Mondrian Process](https://mlsanity.com/paper/2002.00797/) (2020)
- [Isolation Mondrian Forest for Batch and Online Anomaly Detection](https://mlsanity.com/paper/2003.03692/) (2020)
- [Reducing numerical precision preserves classification accuracy in Mondrian Forests](https://mlsanity.com/paper/2106.14340/) (2021)

## Built on by (most cited first, 6 of 6)

- [Autoencoding Random Forests](https://mlsanity.com/paper/2505.21441/) (2025)
- [Exogenous Randomness Empowering Random Forests](https://mlsanity.com/paper/2411.07554/) (2024)
- [Statistical Advantages of Oblique Randomized Decision Trees and Forests](https://mlsanity.com/paper/2407.02458/) (2024)
- [TrIM: Transformed Iterative Mondrian Forests for Gradient-based Dimension Reduction and High-Dimensional Regression](https://mlsanity.com/paper/2407.09964/) (2024)
- [The Uniformly Rotated Mondrian Kernel](https://mlsanity.com/paper/2502.04323/) (2025)
- [CART Random Forests as Sequential Allocation over Random Opportunity Sets: A Stochastic-Control Theory of Ensemble Risk](https://mlsanity.com/paper/2605.26675/) (2026)

## Abstract (arXiv)

Random forests are popular methods for regression and classification analysis, and many different variants have been proposed in recent years. One interesting example is the Mondrian random forest, in which the underlying constituent trees are constructed via a Mondrian process. We give precise bias and variance characterizations, along with a Berry-Esseen-type central limit theorem, for the Mondrian random forest regression estimator. By combining these results with a carefully crafted debiasing approach and an accurate variance estimator, we present valid statistical inference methods for the unknown regression function. These methods come with explicitly characterized error bounds in terms of the sample size, tree complexity parameter, and number of trees in the forest, and include coverage error rates for feasible confidence interval estimators. Our debiasing procedure for the Mondrian random forest also allows it to achieve the minimax-optimal point estimation convergence rate in mean squared error for multivariate β-H"older regression functions, for all β > 0, provided that the underlying tuning parameters are chosen appropriately. Efficient and implementable algorithms are devised for both batch and online learning settings, and we study the computational complexity of different Mondrian random forest implementations. Finally, simulations with synthetic data validate our theory and methodology, demonstrating their excellent finite-sample properties.