Random Jump Forests
Abstract
Random jump forests are introduced as a nonparametric tool for estimating conditional cumulative transition rates and occupation probabilities in multi-state models. The main idea is that a single tree partitions the covariate space for all transitions simultaneously, using partially observed trajectories, and with Nelson--Aalen estimators at the terminal nodes. Occupation probabilities are recovered through the product integral without requiring the Markov assumption. Uniform consistency and a functional central limit theorem for the estimators of cumulative rates can be established under the assumption that the covariate vector takes finitely many values, and under suitable splitting conditions. In particular, pointwise confidence intervals and simultaneous bands are available in the Markov case. Simulation studies show a predictive accuracy close to the correctly specified benchmark models and marked improvements when benchmarks are misspecified, with further illustration on four biomedical data sets. In the coverage study, confidence bands attain near-nominal coverage in several settings, with pooling of heterogeneous rates being the main source of possible undercoverage. The method, including prediction assessment and variable importance, is implemented in the R package JumpForests.
Related
- Random Jump Intensities and Bernstein Density Estimation in Ergodic Basic Affine Jump-Diffusion Processes
- Recursive Stochastic Linear-Quadratic Control with Indefinite Weights for Jump-Diffusion Systems with Random Coefficients
- Dynamics for exclusion processes with random environments of particle jump rates
- Random Hazard Forests
- Wilcoxon Random Forests for Robust Distributional Prediction
BibTeX
@misc{bladt2026random,
title = {{Random Jump Forests}},
author = {Martin Bladt and Rasmus Frigaard Lemvig},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32498},
eprint = {2610.32498},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32498},
}
RIS
TY - UNPB
TI - Random Jump Forests
AU - Martin Bladt
AU - Rasmus Frigaard Lemvig
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32498
UR - https://arxiv.org/abs/2610.32498
AB - Random jump forests are introduced as a nonparametric tool for estimating conditional cumulative transition rates and occupation probabilities in multi-state models. The main idea is that a single tree partitions the covariate space for all transitions simultaneously, using partially observed trajectories, and with Nelson--Aalen estimators at the terminal nodes. Occupation probabilities are recovered through the product integral without requiring the Markov assumption. Uniform consistency and a functional central limit theorem for the estimators of cumulative rates can be established under the assumption that the covariate vector takes finitely many values, and under suitable splitting conditions. In particular, pointwise confidence intervals and simultaneous bands are available in the Markov case. Simulation studies show a predictive accuracy close to the correctly specified benchmark models and marked improvements when benchmarks are misspecified, with further illustration on four biomedical data sets. In the coverage study, confidence bands attain near-nominal coverage in several settings, with pooling of heterogeneous rates being the main source of possible undercoverage. The method, including prediction assessment and variable importance, is implemented in the R package JumpForests.
ER -