# Conditional Distribution Estimation for Functional Responses with Random Forests

arXiv: https://arxiv.org/abs/2608.08247 · HTML: https://mlsanity.com/paper/2608.08247/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 44 references that are in the map.
- First posted on arXiv 8 Aug 2026.

## Builds on (most cited first, 4 of 4)

- [Probabilistic neural operators for functional uncertainty quantification](https://mlsanity.com/paper/2502.12902/) (2025)
- [A spectral mixture representation of isotropic kernels with application to random Fourier features](https://mlsanity.com/paper/2411.02770/) (2024)
- [(f)RFCDE: Random Forests for Conditional Density Estimation and Functional Data](https://mlsanity.com/paper/1906.07177/) (2019)
- [Exceedance and force of centrality for functional data](https://mlsanity.com/paper/2504.02296/) (2025)

## Abstract (arXiv)

Many functional data analyses reduce random functions to scalar summaries or conditional mean curves. This is limiting when we wish to understand how covariates affect the distribution of entire functional responses, including their shape, timing, or variability. We study the problem of estimating conditional laws of functional outcomes and show that these objects can be estimated and evaluated in a practical nonparametric framework. To do this, we introduce functional distributional random forests, which estimate each conditional law as a covariate-dependent distribution over sampled functions by training a random forest to minimize a kernel-based maximum mean discrepancy within the leaf nodes of the decision tree. This supports inference on arbitrary functionals of the conditional distribution while keeping predictive samples tied to realistic curves. We consider a variety of kernels defined on function spaces, including Sobolev and operator-induced kernels. We also provide conditions for consistency of our estimator and develop scoring rules for comparing it to baseline estimators. In simulations, our method recovers distributional changes that are missed by baseline methods. In an application to NHANES accelerometer data, it identifies interesting covariate-associated changes in both median activity profiles and predictive dispersion.