We propose a new inference framework called localized conformal prediction.
It generalizes the framework of conformal prediction by offering a
single-test-sample adaptive construction that emphasizes a local region around
this test sample, and can be combined with different conformal score
constructions. The proposed framework enjoys an assumption-free finite sample
marginal coverage guarantee, and it also offers additional local coverage
guarantees under suitable assumptions. We demonstrate how to change from
conformal prediction to localized conformal prediction using several conformal
scores, and we illustrate a potential gain via numerical examples.

本文提出一种名为局部合规预测的新的推理框架，它通过提供围绕测试样本的局部区域的自适应构建的单次测试样本，以及与不同合规得分结构相结合，来推广合规预测的框架。该框架享有无假设的有限样本边际覆盖保证，并在适当的假设条件下提供额外的局部覆盖保证。我们展示了如何使用多个合规分数从合规预测变为局部合规预测，并通过数值实例说明了潜在的收益。

本地化拟合预测：一种基于推理的拟合预测通用框架

Localized Conformal Prediction: A Generalized Inference Framework for  Conformal Prediction

We propose a new method called localized conformal prediction, where we can
perform conformal inference using only a local region around a new test sample
to construct its confidence interval. Localized conformal inference is a
natural extension to conformal inference. It generalizes the method of
conformal prediction to the case where we can break the data exchangeability,
so as to give the test sample a special role. To our knowledge, this is the
first work that introduces such a localization to the framework of conformal
prediction. We prove that our proposal can also have assumption-free and finite
sample coverage guarantees, and we compare the behaviors of localized conformal
prediction and conformal prediction in simulations.

提出了一种名为局部一致性预测的新方法，它可以仅使用新测试样本周围的局部区域来构建置信区间，旨在将数据互换性打破为测试样本赋予特殊角色的情况下，推广了一致性预测方法，并证明了其假设无关与有限样本覆盖保证，并在模拟中比较了局部一致性预测和一致性预测的行为。