Conformal prediction with localization

TL;DR

This paper introduces localized conformal prediction, a novel method that constructs confidence intervals based on local data regions around test samples, extending conformal inference to non-exchangeable data.

Contribution

It is the first to incorporate localization into conformal prediction, providing assumption-free, finite-sample coverage guarantees and enabling test-specific inference.

Findings

Localized conformal prediction achieves valid coverage in simulations.

The method generalizes conformal prediction to non-exchangeable data.

Simulation results compare the behavior of localized and standard conformal methods.

Abstract

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.