We introduce our method, conformal highest conditional density sets (CHCDS), that forms conformal prediction sets using existing estimated conditional highest density predictive regions. We prove the validity of the method and that conformal adjustment is negligible under some regularity conditions. In particular, if we correctly specify the underlying conditional density estimator, the conformal adjustment will be negligible. When the underlying model is incorrect, the conformal adjustment provides guaranteed nominal unconditional coverage. We compare the proposed method via simulation and a real data analysis to other existing methods. Our numerical results show that the flexibility of being able to use any existing conditional density estimation method is a large advantage for CHCDS compared to existing methods.

翻译：本文提出了一种新方法——保形最高条件密度集（CHCDS），该方法利用现有估计的条件最高密度预测区域构建保形预测集。我们证明了该方法的有效性，并在特定正则性条件下证实保形调整可忽略不计。特别地，若条件密度估计器设定正确，保形调整将趋于微小。当基础模型设定有误时，保形调整仍能保证名义上的无条件覆盖度。通过模拟实验与真实数据分析，我们将所提方法与现有方法进行比较。数值结果表明，CHCDS能够灵活运用任意现有条件密度估计方法，相较于现有方法具有显著优势。