# Distributional Random Forests: Heterogeneity Adjustment and Multivariate Distributional Regression

arXiv: https://arxiv.org/abs/2005.14458 · HTML: https://mlsanity.com/paper/2005.14458/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2020.

## Built on by (most cited first, 30 of 37)

- [Adversarial random forests for density estimation and generative modeling](https://mlsanity.com/paper/2205.09435/) (2022)
- [Doubly Robust Distributionally Robust Off-Policy Evaluation and Learning](https://mlsanity.com/paper/2202.09667/) (2022)
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- [An Efficient Doubly-Robust Test for the Kernel Treatment Effect](https://mlsanity.com/paper/2304.13237/) (2023)
- [Aggregating distribution forecasts from deep ensembles](https://mlsanity.com/paper/2204.02291/) (2022)
- [Confidence and Uncertainty Assessment for Distributional Random Forests](https://mlsanity.com/paper/2302.05761/) (2023)
- [Treeffuser: Probabilistic Predictions via Conditional Diffusions with Gradient-Boosted Trees](https://mlsanity.com/paper/2406.07658/) (2024)
- [Distributional regression and its evaluation with the CRPS: Bounds and convergence of the minimax risk](https://mlsanity.com/paper/2205.04360/) (2022)
- [Efficient and Sharp Off-Policy Evaluation in Robust Markov Decision Processes](https://mlsanity.com/paper/2404.00099/) (2024)
- [Model Free Prediction with Uncertainty Assessment](https://mlsanity.com/paper/2405.12684/) (2024)
- [Online Distributional Regression](https://mlsanity.com/paper/2407.08750/) (2024)
- [Multivariate Latent Recalibration for Conditional Normalizing Flows](https://mlsanity.com/paper/2505.16636/) (2025)
- [MMD-based Variable Importance for Distributional Random Forest](https://mlsanity.com/paper/2310.12115/) (2023)
- [The Generalised Kernel Covariance Measure](https://mlsanity.com/paper/2604.03721/) (2026)
- [Transforming Conditional Density Estimation Into a Single Nonparametric Regression Task](https://mlsanity.com/paper/2511.18530/) (2025)
- [Multivariate Uncertainty Quantification with Tomographic Quantile Forests](https://mlsanity.com/paper/2512.16383/) (2025)
- [A new methodology to predict the oncotype scores based on clinico-pathological data with similar tumor profiles](https://mlsanity.com/paper/2303.06966/) (2023)
- [Generalized Random Forests using Fixed-Point Trees](https://mlsanity.com/paper/2306.11908/) (2023)
- [Simplifying Random Forests' Probabilistic Forecasts](https://mlsanity.com/paper/2408.12332/) (2024)
- [Scoring rule nets: beyond mean target prediction in multivariate regression](https://mlsanity.com/paper/2409.14456/) (2024)
- [Interaction Testing in Variation Analysis](https://mlsanity.com/paper/2411.08861/) (2024)
- [Risk Bounds For Distributional Regression](https://mlsanity.com/paper/2505.09075/) (2025)
- [LILI clustering algorithm: Limit Inferior Leaf Interval Integrated into Causal Forest for Causal Interference](https://mlsanity.com/paper/2507.03271/) (2025)
- [Generative Regression with IQ-BART](https://mlsanity.com/paper/2507.04168/) (2025)
- [Forests of Uncertaint(r)ees: Using tree-based ensembles to estimate probability distributions of future conflict](https://mlsanity.com/paper/2512.06210/) (2025)
- [Distributional Random Forests for Complex Survey Designs](https://mlsanity.com/paper/2512.08179/) (2025)
- [Reliable Real-Time Value at Risk Estimation via Quantile Regression Forest with Conformal Calibration](https://mlsanity.com/paper/2602.01912/) (2026)
- [Nonparametric Distribution Regression Re-calibration](https://mlsanity.com/paper/2602.13362/) (2026)

## Abstract (arXiv)

Random Forest (Breiman, 2001) is a successful and widely used regression and classification algorithm. Part of its appeal and reason for its versatility is its (implicit) construction of a kernel-type weighting function on training data, which can also be used for targets other than the original mean estimation. We propose a novel forest construction for multivariate responses based on their joint conditional distribution, independent of the estimation target and the data model. It uses a new splitting criterion based on the MMD distributional metric, which is suitable for detecting heterogeneity in multivariate distributions. The induced weights define an estimate of the full conditional distribution, which in turn can be used for arbitrary and potentially complicated targets of interest. The method is very versatile and convenient to use, as we illustrate on a wide range of examples. The code is available as Python and R packages drf.