Title: A Few Observations on Sample-Conditional Coverage in Conformal Prediction Show Chinese title

Title: 关于一致性预测中样本条件覆盖率的一些观察

Abstract: We revisit the problem of constructing predictive confidence sets for which we wish to obtain some type of conditional validity. We provide new arguments showing how ``split conformal'' methods achieve near desired coverage levels with high probability, a guarantee conditional on the validation data rather than marginal over it. In addition, we directly consider (approximate) conditional coverage, where, e.g., conditional on a covariate $X$ belonging to some group of interest, we would like a guarantee that a predictive set covers the true outcome $Y$. We show that the natural method of performing quantile regression on a held-out (validation) dataset yields minimax optimal guarantees of coverage here. Complementing these positive results, we also provide experimental evidence that interesting work remains to be done to develop computationally efficient but valid predictive inference methods. Show Chinese abstract

Abstract: 我们重新审视了构建预测置信集的问题，希望获得某种形式的条件有效性。 我们提供了新的论据，表明“分裂一致”方法以高概率实现接近期望的覆盖率，这种保证是基于验证数据的条件，而不是对其边际分布。 此外，我们直接考虑（近似）条件覆盖，例如，当感兴趣的协变量 $X$ 属于某个组时，我们希望得到一个保证，即预测集能覆盖真实结果 $Y$。 我们证明了在保留的（验证）数据集上进行分位数回归的自然方法在这里可以产生最优的覆盖率保证。 作为这些正面结果的补充，我们也提供了实验证据，表明仍有有趣的工作需要完成，以开发计算高效且有效的预测推断方法。