(f)RFCDE: Random Forests for Conditional Density Estimation and Functional Data

TL;DR

This paper introduces (f)RFCDE, an extension of random forests that efficiently estimates conditional densities, handles functional data, and manages multiple responses, providing a more comprehensive uncertainty quantification.

Contribution

It presents a novel method to perform conditional density estimation with random forests, including functional data and multiple responses, without increasing computational complexity.

Findings

Efficiently estimates conditional densities for complex data.

Handles functional covariates and multiple responses.

Provides open-source R and Python software implementations.

Abstract

Random forests is a common non-parametric regression technique which performs well for mixed-type unordered data and irrelevant features, while being robust to monotonic variable transformations. Standard random forests, however, do not efficiently handle functional data and runs into a curse-of dimensionality when presented with high-resolution curves and surfaces. Furthermore, in settings with heteroskedasticity or multimodality, a regression point estimate with standard errors do not fully capture the uncertainty in our predictions. A more informative quantity is the conditional density p(y | x) which describes the full extent of the uncertainty in the response y given covariates x. In this paper we show how random forests can be efficiently leveraged for conditional density estimation, functional covariates, and multiple responses without increasing computational complexity. We provide open-source software for all procedures with R and Python versions that call a common C++ library.