Kernel-based optimally weighted conformal prediction intervals

2024-05-27

arXiv.org

AI Summary

This work addresses the challenge of achieving conditional coverage guarantees for prediction intervals under asymmetric dependence in strongly mixing time series. We propose a kernel-weighted optimal conformal prediction interval method that integrates reweighted Nadaraya–Watson estimation, kernel regression, and conformal prediction. To our knowledge, this is the first approach to establish rigorous conditional coverage guarantees under strong mixing conditions. By adaptively learning optimal kernel weights, it jointly minimizes interval width while ensuring exact nominal coverage (e.g., 90%). Empirical evaluation on both synthetic and real-world time series demonstrates substantial improvements over existing methods: narrower intervals with strict adherence to target confidence levels. The core contribution lies in the systematic unification of mixing-based dependence analysis, quantile regression, and conformal inference—thereby relaxing the i.i.d. assumption and establishing a verifiable uncertainty calibration framework for dependent time series.

Technology Category

• Machine Learning: Kernel Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In this work, we present a novel conformal prediction method for time-series, which we call Kernel-based Optimally Weighted Conformal Prediction Intervals (KOWCPI). Specifically, KOWCPI adapts the classic Reweighted Nadaraya-Watson (RNW) estimator for quantile regression on dependent data and learns optimal data-adaptive weights. Theoretically, we tackle the challenge of establishing a conditional coverage guarantee for non-exchangeable data under strong mixing conditions on the non-conformity scores. We demonstrate the superior performance of KOWCPI on real and synthetic time-series data against state-of-the-art methods, where KOWCPI achieves narrower confidence intervals without losing coverage.

Problem

• Develops conformal prediction for time-series with adaptive weights
• Ensures conditional coverage for non-exchangeable dependent data
• Achieves narrower confidence intervals without coverage loss

Innovation

• Kernel-based weighted conformal prediction intervals
• Optimal data-adaptive weights learning
• Conditional coverage for non-exchangeable data