Topology-Aware Conformal Prediction for Stream Networks
This addresses the problem of accurate uncertainty quantification for researchers and practitioners in environmental science or hydrology dealing with stream networks, representing an incremental improvement over prior conformal prediction methods.
The paper tackled uncertainty quantification in stream networks by proposing STACI, a framework that integrates network topology and temporal dynamics into conformal prediction, resulting in superior performance that balances prediction efficiency and coverage compared to existing methods.
Stream networks, a unique class of spatiotemporal graphs, exhibit complex directional flow constraints and evolving dependencies, making uncertainty quantification a critical yet challenging task. Traditional conformal prediction methods struggle in this setting due to the need for joint predictions across multiple interdependent locations and the intricate spatio-temporal dependencies inherent in stream networks. Existing approaches either neglect dependencies, leading to overly conservative predictions, or rely solely on data-driven estimations, failing to capture the rich topological structure of the network. To address these challenges, we propose Spatio-Temporal Adaptive Conformal Inference (\texttt{STACI}), a novel framework that integrates network topology and temporal dynamics into the conformal prediction framework. \texttt{STACI} introduces a topology-aware nonconformity score that respects directional flow constraints and dynamically adjusts prediction sets to account for temporal distributional shifts. We provide theoretical guarantees on the validity of our approach and demonstrate its superior performance on both synthetic and real-world datasets. Our results show that \texttt{STACI} effectively balances prediction efficiency and coverage, outperforming existing conformal prediction methods for stream networks.