Filtered Conformal Ellipsoids for Graph-Native Time Series

2026-06-15

AI Summary

This work addresses the challenge of simultaneously achieving shape-plausible forecasts and valid coverage in multivariate time series joint prediction. The authors propose a novel approach that integrates state-space modeling with conformal prediction: a GCN-GRU filter learns dynamic mean trajectories and a diagonal-plus-low-rank covariance structure, while split conformal calibration employs Mahalanobis scores to construct data-driven ellipsoidal prediction regions that ensure valid coverage even under non-Gaussian distributions. Theoretically, within the quotient space of observable predictive laws, they establish data-dependent Chebyshev- and Bernstein-type approximate coverage bounds, proving that the resulting conditionally valid ellipsoids nearly attain oracle-level volume efficiency. Experiments on traffic datasets such as METR-LA and PEMS-BAY demonstrate that the proposed method significantly outperforms baselines with static covariances or without filtering, achieving superior sharpness while maintaining accurate coverage.

Abstract

Joint prediction sets for multivariate time series should control a single event while adapting to cross-coordinate dependence. We study filtered conformal ellipsoids: a frozen state-space filter emits a one-step predictive mean and covariance, and split-conformal calibration is applied to the resulting Mahalanobis scores. The filter is used to choose the ellipsoid shape; conformal calibration chooses the scalar radius, so the construction benefits from a learned predictive covariance without relying on Gaussian tail probabilities for coverage. The main difficulty is that filtered scores are dependent and learned recurrent filters need not contract in their raw hidden state; we therefore analyse contraction in an observable predictive-law quotient that identifies hidden states producing the same future sequence of emitted Gaussian laws. Under a stable Bayes Gaussian-projection filter, covariance bounds, and a finite-horizon observability Fisher condition, small excess Gaussian negative log-likelihood implies contraction of the learned emitted laws. Combined with a threshold-autocovariance envelope this yields a Chebyshev-type approximate coverage bound for filtered split-conformal prediction under dependence; a sharper Bernstein-type bound requires an additional geometric-mixing concentration assumption. Under Gaussian oracle realisability we also obtain a near-oracle log-volume comparison within the class of conditionally valid Gaussian ellipsoid rules. We instantiate the framework with a GCN-GRU filter with diagonal-plus-low-rank covariance. On moderate-size graph-native traffic benchmarks (METRLA-$20$ and PEMSBAY-$50$), the learned filter gives sharper at-target ellipsoids than static-covariance and non-filter baselines; at full-graph scale and on non-graph-native datasets, factor and copula baselines can be stronger.

Problem

• conformal prediction
• multivariate time series
• graph-native data
• prediction sets
• dependence

Innovation

• filtered conformal prediction
• graph-native time series
• Mahalanobis calibration
• state-space filtering
• coverage under dependence