Title: Probabilistic Conformal Prediction with Approximate Conditional Validity Show Chinese title

Title: 概率保形预测的近似条件有效性

Abstract: We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and probabilistic conformal prediction, usually provide only a marginal coverage guarantee. In contrast, our approach extends these frameworks to achieve approximately conditional coverage, which is crucial for many practical applications. Our prediction sets adapt to the behavior of the predictive distribution, making them effective even under high heteroscedasticity. While exact conditional guarantees are infeasible without assumptions on the underlying data distribution, we derive non-asymptotic bounds that depend on the total variation distance of the conditional distribution and its estimate. Using extensive simulations, we show that our method consistently outperforms existing approaches in terms of conditional coverage, leading to more reliable statistical inference in a variety of applications. Show Chinese abstract

Abstract: 我们开发了一种新的方法来生成预测集，该方法结合了非形式化方法的灵活性和条件分布$P_{Y \mid X}$的估计。现有的方法，例如非形式化分位数回归和概率非形式化预测，通常只能提供边缘覆盖率保证。相比之下，我们的方法扩展了这些框架以实现近似条件覆盖率，这对许多实际应用至关重要。我们的预测集适应预测分布的行为，即使在高异方差的情况下也使其有效。虽然在没有对潜在数据分布做出假设的情况下，精确的条件保证不可行，但我们推导出非渐近界，这些界依赖于条件分布及其估计之间的总变化距离。通过广泛的模拟，我们表明我们的方法在条件覆盖率方面始终优于现有方法，从而在各种应用中产生更可靠的统计推断。