Conformal Prediction under Levy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbations

TL;DR

This paper introduces a robust conformal prediction framework that models distribution shifts with Levy-Prokhorov ambiguity sets, enabling valid prediction intervals under local and global perturbations, supported by theoretical analysis and real-world experiments.

Contribution

It establishes a novel connection between conformal prediction and Levy-Prokhorov ambiguity sets, allowing for robust prediction intervals under distribution shifts.

Findings

Robust conformal intervals maintain coverage under distribution shifts.

LP ambiguity sets effectively model local and global perturbations.

Experimental results show improved robustness on real datasets.

Abstract

Conformal prediction provides a powerful framework for constructing prediction intervals with finite-sample guarantees, yet its robustness under distribution shifts remains a significant challenge. This paper addresses this limitation by modeling distribution shifts using Levy-Prokhorov (LP) ambiguity sets, which capture both local and global perturbations. We provide a self-contained overview of LP ambiguity sets and their connections to popular metrics such as Wasserstein and Total Variation. We show that the link between conformal prediction and LP ambiguity sets is a natural one: by propagating the LP ambiguity set through the scoring function, we reduce complex high-dimensional distribution shifts to manageable one-dimensional distribution shifts, enabling exact quantification of worst-case quantiles and coverage. Building on this analysis, we construct robust conformal prediction intervals that remain valid under distribution shifts, explicitly linking LP parameters to interval width and confidence levels. Experimental results on real-world datasets demonstrate the effectiveness of the proposed approach.