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Filtered Conformal Ellipsoids for Graph-Native Time Series

NeurIPS 2026 · Time series › Causal and generative time series · approach: Probabilistic and conformal forecasting · 0 citations (OpenAlex)

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Proposes filtered split-conformal ellipsoids: a frozen GCN-GRU filter supplies predictive covariance shape, conformal calibration of squared Mahalanobis scores sets the radius, with a dependent-data marginal coverage-gap bound and empirical gains on graph-native traffic.

Problem

Joint prediction sets for multivariate time series must control a single joint event while adapting to cross-coordinate dependence, but calibration scores are dependent and learned recurrent filters may not contract in raw state.

Approach

Use a frozen learned state-space filter's one-step predictive Gaussian only for ellipsoid shape, calibrate the scalar radius by split-conformal on Mahalanobis scores, and analyse contraction on each filter's own observable predictive-law quotient rather than raw hidden states.

Key results

• GNF reaches wproj 3.05 at joint coverage 0.910 on METR-LA-20, 23.6% below StaticCGIF (3.99).
• On PeMS-BAY-50, GNF reaches wproj 1.98 at joint coverage 0.904, 40.5% below StaticCGIF (3.33).
• At full-graph scale (PeMS-BAY-325) GNF under-covers (0.878) without ACI, and factor baselines (ACI-PerGroup-FactorCGIF, wproj 5.64) are sharper under graph-aware GPVAR backbone.

Surprising findings

• Factor and copula baselines beat the learned filter at full-graph scale and on non-graph-native datasets.
• A matched-budget rank-4 DeepVAR-style control undercovers and is wider than the learned filter on both headline cells.

Limitations

• Theory is a conditional chain; contraction and observability premises are not verified for arbitrary trained GRUs, and guarantees are marginal rather than calibration-conditional.
• Sharpness advantage holds only at moderate N on graph-native traffic; full-graph and non-graph-native cells favour factor/copula baselines.
• Shared node-wise recurrence may lose node-specific information at large N.

Experimental setup

Datasets: METR-LA PeMS-BAY Solar LOOP Seattle ETT Jena

Benchmarks: METR-LA (N=20) PeMS-BAY (N=50) METR-LA (N=207) PeMS-BAY (N=325) Solar LOOP Seattle ETT Jena

Metrics: mean coordinate-projection length joint coverage normalised log-volume

Baselines: StaticCGIF KalmanFCP DiagGRU GCN rank-zero CopulaCPTS MultiDimSPCI ACI AgACI DeepVAR HopCPT

Builds on: split conformal prediction SPCI CopulaCPTS ACI DeepVAR

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