Conformal Prediction under L'evy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbations

2025-02-19

AI Summary

研究莱维-普罗霍罗夫分布偏移下的保形预测，通过LP模糊集建模局部和全局扰动，构建鲁棒预测区间，实验验证有效性。

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Applications
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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 L'evy-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.

Problem

• Robustness of conformal prediction under distribution shifts
• Modeling local and global perturbations via LP ambiguity sets
• Constructing valid prediction intervals under distributional uncertainties

Innovation

• Lévy-Prokhorov ambiguity sets model distribution shifts
• Propagating ambiguity through scoring reduces dimensionality
• Constructing robust conformal intervals with exact coverage guarantees