Predictive models make mistakes. Hence, there is a need to quantify the uncertainty associated with their predictions. Conformal inference has emerged as a powerful tool to create statistically valid prediction regions around point predictions, but its naive application to regression problems yields non-adaptive regions. New conformal scores, often relying upon quantile regressors or conditional density estimators, aim to address this limitation. Although they are useful for creating prediction bands, these scores are detached from the original goal of quantifying the uncertainty around an arbitrary predictive model. This paper presents a new, model-agnostic family of methods to calibrate prediction intervals for regression problems with local coverage guarantees. Our approach is based on pursuing the coarsest partition of the feature space that approximates conditional coverage. We create this partition by training regression trees and Random Forests on conformity scores. Our proposal is versatile, as it applies to various conformity scores and prediction settings and demonstrates superior scalability and performance compared to established baselines in simulated and real-world datasets. We provide a Python package clover that implements our methods using the standard scikit-learn interface.

翻译：预测模型难免会出错，因此需要量化其预测结果的不确定性。共形推断已成为围绕点预测构建统计有效预测区域的强大工具，但在回归问题中的直接应用会产生非自适应区域。为解决这一局限，学界提出了新的共形得分，这类得分通常依赖于分位数回归或条件密度估计量。虽然这些方法有助于构建预测带，但它们偏离了量化任意预测模型不确定性的原始目标。本文提出了一种新的、与模型无关的方法体系，用于校准回归问题中具有局部覆盖保证的预测区间。我们的方法通过追求特征空间的最粗粒度划分来逼近条件覆盖——具体做法是在共形得分上训练回归树和随机森林以构建该划分。该方案通用性强，可适用于多种共形得分和预测场景，并在模拟与实际数据集上展现出优于现有基线的可扩展性与性能。我们提供了基于标准scikit-learn接口实现的Python包clover。