We develop a new method for creating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Most existing methods, such as conformalized quantile regression and probabilistic conformal prediction, only offer marginal coverage guarantees. Our approach extends these methods to achieve conditional coverage, which is essential for many practical applications. While exact conditional guarantees are impossible without assumptions on the data distribution, we provide non-asymptotic bounds that explicitly depend on the quality of the available estimate of the conditional distribution. Our confidence sets are highly adaptive to the local structure of the data, making them particularly useful in high heteroskedasticity situations. We demonstrate the effectiveness of our approach through extensive simulations, showing that it outperforms existing methods in terms of conditional coverage and improves the reliability of statistical inference in a wide range of applications.

我们开发了一种新方法来创建预测集，它结合了符合性方法的灵活性和条件分布P（Y | X）的估计。我们的方法扩展了现有方法，实现了条件覆盖，这对许多实际应用至关重要。我们提供了非渐近界限，明确依赖于对条件分布的可用估计的质量，使得我们的置信集在数据的局部结构上高度自适应，特别适用于高异方差情况。通过广泛的模拟，我们证明了我们的方法的有效性，显示其在条件覆盖和统计推断的可靠性方面优于现有方法，在各种应用中提高了统计推断的可靠性。

有条件有效的概率拟合预测