# Confidence and Uncertainty Assessment for Distributional Random Forests

arXiv: https://arxiv.org/abs/2302.05761 · HTML: https://mlsanity.com/paper/2302.05761/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 47 references that are in the map.
- First posted on arXiv 11 Feb 2023.

## Builds on (most cited first, 12 of 12)

- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2002.03689/) (2020)
- [Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regression](https://mlsanity.com/paper/2102.08208/) (2021)
- [Distributional Random Forests: Heterogeneity Adjustment and Multivariate Distributional Regression](https://mlsanity.com/paper/2005.14458/) (2020)
- [Metrizing Weak Convergence with Maximum Mean Discrepancies](https://mlsanity.com/paper/2006.09268/) (2020)
- [Closed-form Expressions for Maximum Mean Discrepancy with Applications to Wasserstein Auto-Encoders](https://mlsanity.com/paper/1901.03227/) (2019)
- [Extended Conditional Independence and Applications in Causal Inference](https://mlsanity.com/paper/1512.00245/) (2015)
- [Benchmarking Regression Methods: A comparison with CGAN](https://mlsanity.com/paper/1905.12868/) (2019)

## Built on by (most cited first, 5 of 5)

- [Model Free Prediction with Uncertainty Assessment](https://mlsanity.com/paper/2405.12684/) (2024)
- [Conditional Distributional Treatment Effects: Doubly Robust Estimation and Testing](https://mlsanity.com/paper/2603.16829/) (2026)
- [MMD-based Variable Importance for Distributional Random Forest](https://mlsanity.com/paper/2310.12115/) (2023)
- [Multivariate Uncertainty Quantification with Tomographic Quantile Forests](https://mlsanity.com/paper/2512.16383/) (2025)
- [Wasserstein Causal Forests for Distribution-Valued Outcomes](https://mlsanity.com/paper/2609.35898/) (2026)

## Abstract (arXiv)

The Distributional Random Forest (DRF) is a recently introduced Random Forest algorithm to estimate multivariate conditional distributions. Due to its general estimation procedure, it can be employed to estimate a wide range of targets such as conditional average treatment effects, conditional quantiles, and conditional correlations. However, only results about the consistency and convergence rate of the DRF prediction are available so far. We characterize the asymptotic distribution of DRF and develop a bootstrap approximation of it. This allows us to derive inferential tools for quantifying standard errors and the construction of confidence regions that have asymptotic coverage guarantees. In simulation studies, we empirically validate the developed theory for inference of low-dimensional targets and for testing distributional differences between two populations.