Conformal Prediction for Distributed Data

Conformal prediction is a powerful framework for constructing distribution-free prediction regions with guaranteed coverage. Existing conformal prediction methods are often developed in a centralized setting, assuming that all data are accessible at a single location. However, data are often distributed across multiple machines due to communication constraints or data access restrictions, making conventional conformal prediction methods infeasible. In this paper, we propose a distributed conformal prediction method that leverages random forests without centralizing raw data. To construct prediction sets, we design a communication-efficient distributed quantile estimation algorithm using binary search. Additionally, we investigate a distributed conformalized quantile regression approach that adapts the lengths of prediction sets to heteroscedasticity. To improve predictive efficiency, especially under complex error distributions such as skewed or multimodal structures, we further introduce a distributed conformal prediction method based on highest density sets, yielding narrower and more informative prediction regions. We establish upper and lower bounds on the coverage of the proposed methods. Numerical simulations and an illustrative airline data example demonstrate the effectiveness of our methods.