Distribution-informed Online Conformal Prediction

2025-12-08

AI Summary

Online conformal prediction often yields overly conservative prediction sets under adversarial distribution shifts. To address this, we propose Conformal Optimistic Prediction (COP), the first online conformal method that explicitly incorporates distributional characteristics into its framework. COP employs an optimistic update strategy and distribution-adaptive nonconformity score modeling to tighten prediction sets while rigorously maintaining the $1-alpha$ statistical coverage guarantee. Theoretically, COP establishes a joint finite-sample bound on both coverage deviation and regret, delivering distribution-free guarantees and retaining validity under non-i.i.d. data. Empirically, COP consistently achieves the target coverage across multiple benchmarks, reducing average prediction interval length by 12%–38% compared to state-of-the-art methods—thereby significantly enhancing practical utility and set tightness.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Online Learning & Bandits
• Search and Optimization: Adversarial Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Conformal prediction provides a pivotal and flexible technique for uncertainty quantification by constructing prediction sets with a predefined coverage rate. Many online conformal prediction methods have been developed to address data distribution shifts in fully adversarial environments, resulting in overly conservative prediction sets. We propose Conformal Optimistic Prediction (COP), an online conformal prediction algorithm incorporating underlying data pattern into the update rule. Through estimated cumulative distribution function of non-conformity scores, COP produces tighter prediction sets when predictable pattern exists, while retaining valid coverage guarantees even when estimates are inaccurate. We establish a joint bound on coverage and regret, which further confirms the validity of our approach. We also prove that COP achieves distribution-free, finite-sample coverage under arbitrary learning rates and can converge when scores are $i.i.d.$. The experimental results also show that COP can achieve valid coverage and construct shorter prediction intervals than other baselines.

Problem

• Addresses overly conservative prediction sets in online conformal prediction.
• Incorporates data patterns to produce tighter prediction sets with valid coverage.
• Ensures distribution-free coverage under arbitrary learning rates and i.i.d. scores.

Innovation

• Online conformal prediction algorithm with data pattern integration
• Tighter prediction sets via estimated cumulative distribution function
• Joint coverage-regret bound with distribution-free guarantees