标题： 用于连续有界结果的共形化回归 显示英文标题

标题： Conformalized Regression for Continuous Bounded Outcomes

摘要： 回归问题中，有界的连续结果在现实世界的统计和机器学习应用中经常出现，例如对比率和比例的分析。 在这种情况下，一个核心挑战是预测与新协变量值相关的结果。 现有的统计和机器学习文献大多专注于有界结果的点预测，或者基于渐近近似的区间预测。 我们基于转换模型和贝塔回归，开发了用于有界结果的共形预测区间。 我们引入了与底层模型一致的残差非一致性度量，并考虑了有界结果回归设置中的固有异方差性。 我们在完全共形预测的背景下提出了关于渐近边缘和条件有效性的理论结果，该结果在模型误指的情况下仍然有效。 对于分割共形预测，我们基于全面的模拟研究提供了经验覆盖分析。 模拟研究显示，这两种方法在有限样本下都能提供有效的预测覆盖，包括模型误指的情况。 最后，我们在真实数据上展示了所提出的共形预测区间的实际性能，并将其与基于引导的替代方法进行了比较。 显示英文摘要

摘要： Regression problems with bounded continuous outcomes frequently arise in real-world statistical and machine learning applications, such as the analysis of rates and proportions. A central challenge in this setting is predicting a response associated with a new covariate value. Most of the existing statistical and machine learning literature has focused either on point prediction of bounded outcomes or on interval prediction based on asymptotic approximations. We develop conformal prediction intervals for bounded outcomes based on transformation models and beta regression. We introduce tailored non-conformity measures based on residuals that are aligned with the underlying models, and account for the inherent heteroscedasticity in regression settings with bounded outcomes. We present a theoretical result on asymptotic marginal and conditional validity in the context of full conformal prediction, which remains valid under model misspecification. For split conformal prediction, we provide an empirical coverage analysis based on a comprehensive simulation study. The simulation study demonstrates that both methods provide valid finite-sample predictive coverage, including settings with model misspecification. Finally, we demonstrate the practical performance of the proposed conformal prediction intervals on real data and compare them with bootstrap-based alternatives.