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Topology-Aware Conformal Prediction for Stream Networks

NeurIPS 2025 · Probabilistic and scientific modeling › Molecules and proteins · approach: Flow matching generative modeling · 0 citations (OpenAlex)

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Proposes STACI, an adaptive conformal prediction framework for stream networks that mixes sample and tail-up topology-induced covariance into a Mahalanobis nonconformity score and applies ACI for distribution shift.

Problem

Joint uncertainty quantification for multivariate spatio-temporal forecasts on stream networks, where conventional conformal prediction either ignores inter-site dependencies (overly conservative sets) or relies only on sample covariance (unstable, under-covering under temporal shift).

Approach

A nonconformity score based on a Mahalanobis distance whose matrix linearly combines the inverse sample residual covariance and an inverse covariance derived from a tail-up stream-network model (flow-connected exponential decay with flow weights), plus ACI-style online update of the miscoverage level.

Key results

• On PeMS-G1 with AGCRN, STACI (gamma=0.01) reaches 95.75% coverage with inefficiency 67.54 vs 73.82 for MultiDimSPCI (which under-covers at 92.92%).
• On PeMS-G2 with ASTGCN, STACI (gamma=0.01) achieves 95.05% coverage with inefficiency 58.07, the lowest among the compared CP methods.
• Without ACI (gamma=0), STACI lifts coverage from under 87% to above 95% with only a marginal efficiency cost, according to the authors.

Measured effects reported in the paper

Surprising findings

• Sample-covariance-based MultiDimSPCI under-covers (about 91-93%) on PeMS despite being the most efficient baseline in some settings.
• Sphere-based and square-based sets over-cover, producing larger volumes than the ellipsoidal methods.

Limitations

• Targets moderate-size subgraphs (about 2 to 30 dimensions); full high-dimensional networks are not handled.
• Theoretical coverage bound depends on estimation-quality and A_n convergence assumptions; finite-sample guarantees under adaptive calibration are left open.
• Experiments limited to two PeMS subnetworks of 12 sensors each and synthetic data.

Experimental setup

Datasets: PeMS (PeMS-G1, PeMS-G2 California highway subnetworks) synthetic tail-up stream network data

Benchmarks: PeMS-G1 PeMS-G2 synthetic tail-up stream network

Metrics: coverage efficiency (ellipsoid volume)^(1/I) inefficiency

Baselines: Sphere Sphere-ACI Square GT MultiDimSPCI MultiDimSPCI (local) CopulaCPTS DeepSTUQ

Builds on: Adaptive Conformal Inference MultiDimSPCI tail-up model

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