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arXiv · 2510.04299

Out-of-bag prediction balls for random forests in metric spaces

Diego Serrano·Eduardo García-Portugués
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Abstract

Statistical methods for metric spaces provide a general and versatile framework for analyzing complex data types. We introduce a novel approach for constructing confidence regions around new predictions from any bagged regression algorithm with metric-space-valued responses. This includes the recent extensions of random forests for metric responses: Fréchet random forests (Capitaine et al., 2024), random forest weighted local constant Fréchet regression (Qiu et al., 2024), and metric random forests (Bulté and Sørensen, 2024). Our prediction regions leverage out-of-bag observations generated during a single forest training, employing the entire data set for both prediction and uncertainty quantification. We establish asymptotic guarantees of out-of-bag prediction balls for four coverage types under certain regularity conditions. Moreover, we demonstrate the superior stability and smaller radius of out-of-bag balls compared to split-conformal methods through extensive numerical experiments where the response lies on the Euclidean space, sphere, hyperboloid, and space of positive definite matrices. A real data application illustrates the potential of the confidence regions for quantifying the uncertainty in the study of solar dynamics and the use of data-driven non-isotropic distances on the sphere.

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Diego Serrano, Eduardo García-Portugués. 2026-04-03. Out-of-bag prediction balls for random forests in metric spaces. https://arxiv.org/abs/2510.04299

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