Robust Conformal Prediction Using Privileged Information

TL;DR

This paper introduces a robust conformal prediction method that leverages privileged information available during training to maintain coverage guarantees despite data corruptions and distribution shifts.

Contribution

It presents a novel weighted conformal prediction framework that incorporates privileged information to handle corruptions, with theoretical guarantees and improved empirical performance.

Findings

Achieves valid coverage rate under data corruptions

Constructs more informative prediction sets than existing methods

Provides theoretical coverage guarantees for the proposed approach

Abstract

We develop a method to generate prediction sets with a guaranteed coverage rate that is robust to corruptions in the training data, such as missing or noisy variables. Our approach builds on conformal prediction, a powerful framework to construct prediction sets that are valid under the i.i.d assumption. Importantly, naively applying conformal prediction does not provide reliable predictions in this setting, due to the distribution shift induced by the corruptions. To account for the distribution shift, we assume access to privileged information (PI). The PI is formulated as additional features that explain the distribution shift, however, they are only available during training and absent at test time. We approach this problem by introducing a novel generalization of weighted conformal prediction and support our method with theoretical coverage guarantees. Empirical experiments on both real and synthetic datasets indicate that our approach achieves a valid coverage rate and constructs more informative predictions compared to existing methods, which are not supported by theoretical guarantees.