Post-Training Adaptive Conformal Prediction for Incomplete Time Series

Abstract

Conformal Prediction (CP) is widely used for uncertainty quantification but faces significant challenges with time series due to non-exchangeability. The issue is exacerbated by missing data, where the exponential growth of missing patterns makes existing approaches computationally expensive and unable to adequately represent each missing pattern. To address this, we propose a novel approach that uses a post-training Neural Network (NN) to handle temporal dependencies and structured missingness in time series data. With a novel non-conformity score function, our method improves conditional coverage for different missing patterns, ensuring prediction intervals are both reliable and informative. We introduce features that capture different missingness mechanisms, enabling the model to adapt to various patterns. Theoretically, we establish asymptotic validity for conditional coverage with adaptive adjustments. Experiments on semi-synthetic benchmarks demonstrate the method's efficiency in producing tight prediction intervals while maintaining group conditional coverage.