# Distributional Random Forests for Complex Survey Designs

arXiv: https://arxiv.org/abs/2512.08179 · HTML: https://mlsanity.com/paper/2512.08179/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 99 references that are in the map.
- First posted on arXiv 9 Dec 2025.

## Builds on (most cited first, 20 of 20)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [A Random Forest Guided Tour](https://mlsanity.com/paper/1511.05741/) (2015)
- [Distributional Random Forests: Heterogeneity Adjustment and Multivariate Distributional Regression](https://mlsanity.com/paper/2005.14458/) (2020)
- [Deep Compositional Spatial Models](https://mlsanity.com/paper/1906.02840/) (2019)
- [Random Forest Weighted Local Fr'echet Regression with Random Objects](https://mlsanity.com/paper/2202.04912/) (2022)
- [Kernel k-Groups via Hartigan's Method](https://mlsanity.com/paper/1710.09859/) (2017)
- [Large sample analysis of the median heuristic](https://mlsanity.com/paper/1707.07269/) (2017)
- [Randomization Can Reduce Both Bias and Variance: A Case Study in Random Forests](https://mlsanity.com/paper/2402.12668/) (2024)
- [Forest Guided Smoothing](https://mlsanity.com/paper/2103.05092/) (2021)
- [Kernel Biclustering algorithm in Hilbert Spaces](https://mlsanity.com/paper/2208.03675/) (2022)
- [Screening for Diabetes Mellitus in the U.S. Population Using Neural Network Models and Complex Survey Designs](https://mlsanity.com/paper/2403.19752/) (2024)
- [Bootstrap inference for the finite population total under complex sampling designs](https://mlsanity.com/paper/1901.01645/) (2019)
- [Hypothesis testing for matched pairs with missing data by maximum mean discrepancy: An application to continuous glucose monitoring](https://mlsanity.com/paper/2206.01590/) (2022)
- [MMD-based Variable Importance for Distributional Random Forest](https://mlsanity.com/paper/2310.12115/) (2023)
- [Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spaces](https://mlsanity.com/paper/2507.15741/) (2025)
- [A unified principled framework for resampling based on pseudo-populations: asymptotic theory](https://mlsanity.com/paper/1705.03827/) (2017)
- [Design-Based Ratio Estimators and Central Limit Theorems for Clustered, Blocked RCTs](https://mlsanity.com/paper/2002.01146/) (2020)
- [Function on Scalar Regression with Complex Survey Designs](https://mlsanity.com/paper/2511.05487/) (2025)

## Abstract (arXiv)

We study estimation of the conditional law P(Y|X = x) and continuous measurable maps of it when Y ∈ Y takes values in a locally compact Polish space (e.g., ℝd), X ∈ ℝp, and the observations arise from a complex survey design: a single- or multi-stage sampling scheme that may involve unequal selection, stratification, and clustering. We propose a survey-calibrated distributional random forest (SDRF) that incorporates complex-design features via the pseudo-population bootstrap, PSU-level honesty, and a Maximum Mean Discrepancy (MMD) split criterion computed from kernel mean embeddings of design-weighted node distributions. We provide a framework for analyzing forest-based estimators under various survey designs; establish consistency for both finite- and super-population conditional laws under explicit conditions on the design, kernel, resampling multipliers, and tree partitions. As far as we are aware, these are the first results on model-free estimation of conditional distributions under survey designs. Simulations under a stratified two-stage cluster design expose the systematic bias incurred by ignoring survey structure. We illustrate the broad applicability of SDRF on NHANES, estimating the conditional joint tolerance regions for two diabetes biomarkers, revealing subgroup-level distributional heterogeneity relevant to diabetes risk profiling in the U.S. population.