Conformal prediction with localization

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 to the setting where we want to perform conformal inference adaptively. We prove that our proposal can also have assumption-free and finite sample coverage guarantees, and we compare the behaviors of localized conformal inference and conformal inference in simulations. To our knowledge, this is the first work that 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.