Conformal Prediction under Levy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbations
This work addresses the problem of ensuring reliable uncertainty quantification in machine learning under distribution shifts for practitioners, representing an incremental improvement by extending conformal prediction with a specific ambiguity set.
The paper tackles the challenge of making conformal prediction robust to distribution shifts by modeling shifts using Levy-Prokhorov ambiguity sets, which capture local and global perturbations, and constructs robust prediction intervals that remain valid under such shifts, with experimental validation on real-world datasets.
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.