mlsanityData to 14 Oct 2026

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

arXiv 2407.09964 ↗First posted 13 Jul 2024math.ST stat.ML stat.THcited by 1

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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.

Key facts. Cited by 1 paper 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.

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19 of 61 references.

References · 19

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  6. 2014Mondrian Forests: Efficient Online Random Forestscited by 25
  7. 2022Mechanism of feature learning in deep fully connected networks and kernel machines that recursively learn featurescited by 25
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  9. 2016The Mondrian Kernelcited by 11
  10. 2015Mondrian Forests for Large-Scale Regression when Uncertainty Matterscited by 9
  11. 2019Scalable and Efficient Hypothesis Testing with Random Forestscited by 8
  12. 2019Random Tessellation Forestscited by 7
7 more
  1. 2020Stochastic geometry to generalize the Mondrian Processcited by 7
  2. 2023Inference with Mondrian Random Forestscited by 6
  3. 2020Learning functions varying along a central subspacecited by 4
  4. 2021Minimax Rates for High-Dimensional Random Tessellation Forestscited by 4
  5. 2022Towards a Unified Framework for Uncertainty-aware Nonlinear Variable Selection with Theoretical Guaranteescited by 4
  6. 2021Dimension Reduction Forests: Local Variable Importance using Structured Random Forestscited by 3
  7. 2024Statistical Advantages of Oblique Randomized Decision Trees and Forestscited by 1

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  1. 2025The Uniformly Rotated Mondrian Kernelcited by 0