# TrIM: Transformed Iterative Mondrian Forests for Gradient-based Dimension Reduction and High-Dimensional Regression

arXiv: https://arxiv.org/abs/2407.09964 · HTML: https://mlsanity.com/paper/2407.09964/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 61 references that are in the map.
- First posted on arXiv 13 Jul 2024.

## Builds on (most cited first, 19 of 19)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison](https://mlsanity.com/paper/1703.00512/) (2017)
- [Unrestricted Permutation forces Extrapolation: Variable Importance Requires at least One More Model, or There Is No Free Variable Importance](https://mlsanity.com/paper/1905.03151/) (2019)
- [Iterative Random Forests to detect predictive and stable high-order interactions](https://mlsanity.com/paper/1706.08457/) (2017)
- [Mondrian Forests: Efficient Online Random Forests](https://mlsanity.com/paper/1406.2673/) (2014)
- [Mechanism of feature learning in deep fully connected networks and kernel machines that recursively learn features](https://mlsanity.com/paper/2212.13881/) (2022)
- [Minimax optimal rates for Mondrian trees and forests](https://mlsanity.com/paper/1803.05784/) (2018)
- [The Mondrian Kernel](https://mlsanity.com/paper/1606.05241/) (2016)
- [Mondrian Forests for Large-Scale Regression when Uncertainty Matters](https://mlsanity.com/paper/1506.03805/) (2015)
- [Scalable and Efficient Hypothesis Testing with Random Forests](https://mlsanity.com/paper/1904.07830/) (2019)
- [Random Tessellation Forests](https://mlsanity.com/paper/1906.05440/) (2019)
- [Stochastic geometry to generalize the Mondrian Process](https://mlsanity.com/paper/2002.00797/) (2020)
- [Inference with Mondrian Random Forests](https://mlsanity.com/paper/2310.09702/) (2023)
- [Learning functions varying along a central subspace](https://mlsanity.com/paper/2001.07883/) (2020)
- [Minimax Rates for High-Dimensional Random Tessellation Forests](https://mlsanity.com/paper/2109.10541/) (2021)
- [Towards a Unified Framework for Uncertainty-aware Nonlinear Variable Selection with Theoretical Guarantees](https://mlsanity.com/paper/2204.07293/) (2022)
- [Dimension Reduction Forests: Local Variable Importance using Structured Random Forests](https://mlsanity.com/paper/2103.13233/) (2021)
- [Statistical Advantages of Oblique Randomized Decision Trees and Forests](https://mlsanity.com/paper/2407.02458/) (2024)

## Built on by (most cited first, 1 of 1)

- [The Uniformly Rotated Mondrian Kernel](https://mlsanity.com/paper/2502.04323/) (2025)

## Abstract (arXiv)

We propose a computationally efficient algorithm for gradient-based linear dimension reduction and high-dimensional regression. The algorithm initially computes a Mondrian forest and uses this estimator to identify a relevant feature subspace of the inputs from an estimate of the expected gradient outer product (EGOP) of the regression function. In addition, we introduce an iterative approach known as Transformed Iterative Mondrian (TrIM) forest to improve the Mondrian forest estimator by using the EGOP estimate to update the set of features and weights used by the Mondrian partitioning mechanism. We obtain consistency guarantees and convergence rates for estimating the EGOP matrix and the random forest estimator obtained from one iteration of the TrIM algorithm. Lastly, we demonstrate the effectiveness of our proposed algorithm for learning the relevant feature subspace across various settings with both simulated and real data.