# Multivariate Prediction Intervals for Random Forests

arXiv: https://arxiv.org/abs/2205.02260 · HTML: https://mlsanity.com/paper/2205.02260/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 36 references that are in the map.
- First posted on arXiv 4 May 2022.

## Builds on (most cited first, 10 of 10)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Batched Large-scale Bayesian Optimization in High-dimensional Spaces](https://mlsanity.com/paper/1706.01445/) (2017)
- [Confidence Intervals for Random Forests: The Jackknife and the Infinitesimal Jackknife](https://mlsanity.com/paper/1311.4555/) (2013)
- [Machine learning pipeline for battery state of health estimation](https://mlsanity.com/paper/2102.00837/) (2021)
- [Valid prediction intervals for regression problems](https://mlsanity.com/paper/2107.00363/) (2021)
- [High-Dimensional Materials and Process Optimization using Data-driven Experimental Design with Well-Calibrated Uncertainty Estimates](https://mlsanity.com/paper/1704.07423/) (2017)
- [Nested Conformal Prediction Sets for Classification with Applications to Probation Data](https://mlsanity.com/paper/2104.09358/) (2021)
- [Autonomous discovery of battery electrolytes with robotic experimentation and machine-learning](https://mlsanity.com/paper/2001.09938/) (2019)
- [A Unified Framework for Random Forest Prediction Error Estimation](https://mlsanity.com/paper/1912.07435/) (2019)
- [Machine Learning with Knowledge Constraints for Process Optimization of Open-Air Perovskite Solar Cell Manufacturing](https://mlsanity.com/paper/2110.01387/) (2021)

## Abstract (arXiv)

Accurate uncertainty estimates can significantly improve the performance of iterative design of experiments, as in Sequential and Reinforcement learning. For many such problems in engineering and the physical sciences, the design task depends on multiple correlated model outputs as objectives and/or constraints. To better solve these problems, we propose a recalibrated bootstrap method to generate multivariate prediction intervals for bagged models and show that it is well-calibrated. We apply the recalibrated bootstrap to a simulated sequential learning problem with multiple objectives and show that it leads to a marked decrease in the number of iterations required to find a satisfactory candidate. This indicates that the recalibrated bootstrap could be a valuable tool for practitioners using machine learning to optimize systems with multiple competing targets.