Distributional Random Forests for Complex Survey Designs on Reproducing Kernel Hilbert Spaces
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911356176826368 |
|---|---|
| author | Zou, Yating Matabuena, Marcos Kosorok, Michael R. |
| author_facet | Zou, Yating Matabuena, Marcos Kosorok, Michael R. |
| contents | We study estimation of the conditional law $P(Y|X=x)$ and continuous functionals $Ψ(P(Y|X=x))$ when $Y$ takes values in a locally compact Polish space, $X \in \mathbb{R}^p$, and the observations arise from a complex survey design. We propose a survey-calibrated distributional random forest (SDRF) that incorporates complex-design features via a pseudo-population bootstrap, PSU-level honesty, and a Maximum Mean Discrepancy (MMD) split criterion computed from kernel mean embeddings of Hájek-type (design-weighted) node distributions. We provide a framework for analyzing forest-style estimators under survey designs; establish design consistency for the finite-population target and model consistency for the super-population target 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 provide finite sample performance and demonstrate the statistical error price of ignoring the survey design. The broad applicability of SDRF is demonstrated using NHANES: We estimate the tolerance regions of the conditional joint distribution of two diabetes biomarkers, illustrating how distributional heterogeneity can support subgroup-specific risk profiling for diabetes mellitus in the U.S. population. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08179 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distributional Random Forests for Complex Survey Designs on Reproducing Kernel Hilbert Spaces Zou, Yating Matabuena, Marcos Kosorok, Michael R. Methodology Machine Learning We study estimation of the conditional law $P(Y|X=x)$ and continuous functionals $Ψ(P(Y|X=x))$ when $Y$ takes values in a locally compact Polish space, $X \in \mathbb{R}^p$, and the observations arise from a complex survey design. We propose a survey-calibrated distributional random forest (SDRF) that incorporates complex-design features via a pseudo-population bootstrap, PSU-level honesty, and a Maximum Mean Discrepancy (MMD) split criterion computed from kernel mean embeddings of Hájek-type (design-weighted) node distributions. We provide a framework for analyzing forest-style estimators under survey designs; establish design consistency for the finite-population target and model consistency for the super-population target 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 provide finite sample performance and demonstrate the statistical error price of ignoring the survey design. The broad applicability of SDRF is demonstrated using NHANES: We estimate the tolerance regions of the conditional joint distribution of two diabetes biomarkers, illustrating how distributional heterogeneity can support subgroup-specific risk profiling for diabetes mellitus in the U.S. population. |
| title | Distributional Random Forests for Complex Survey Designs on Reproducing Kernel Hilbert Spaces |
| topic | Methodology Machine Learning |
| url | https://arxiv.org/abs/2512.08179 |