# Universal consistency and minimax rates for online Mondrian Forests

arXiv: https://arxiv.org/abs/1711.02887 · HTML: https://mlsanity.com/paper/1711.02887/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Nov 2017.

## Built on by (most cited first, 2 of 2)

- [Minimax-optimal and Locally-adaptive Online Nonparametric Regression](https://mlsanity.com/paper/2410.03363/) (2024)
- [Minimax Rates and Spectral Distillation for Tree Ensembles](https://mlsanity.com/paper/2605.11841/) (2026)

## Abstract (arXiv)

We establish the consistency of an algorithm of Mondrian Forests, a randomized classification algorithm that can be implemented online. First, we amend the original Mondrian Forest algorithm, that considers a fixed lifetime parameter. Indeed, the fact that this parameter is fixed hinders the statistical consistency of the original procedure. Our modified Mondrian Forest algorithm grows trees with increasing lifetime parameters λn, and uses an alternative updating rule, allowing to work also in an online fashion. Second, we provide a theoretical analysis establishing simple conditions for consistency. Our theoretical analysis also exhibits a surprising fact: our algorithm achieves the minimax rate (optimal rate) for the estimation of a Lipschitz regression function, which is a strong extension of previous results to an arbitrary dimension.