Filtered Conformal Ellipsoids for Graph-Native Time Series

A new method for constructing joint prediction sets for multivariate time series uses filtered conformal ellipsoids, adapting to cross-coordinate dependence without relying on Gaussian tail probabilities for coverage, according to a paper submitted on 15 June 2026 [1]. The approach, detailed on arXiv, freezes a state-space filter to emit a one-step predictive mean and covariance, then applies split-conformal calibration to the resulting Mahalanobis scores [1]. The filter determines the ellipsoid shape, while conformal calibration selects the scalar radius, allowing the construction to benefit from a learned predictive covariance [1]. The paper addresses a core difficulty: filtered scores are dependent and learned recurrent filters need not contract in their raw hidden state. The authors analyze contraction in an observable predictive-law quotient that identifies hidden states producing the same future sequence of emitted Gaussian laws [2]. 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 [2]. The framework is instantiated with a GCN-GRU filter using diagonal-plus-low-rank covariance [1]. On moderate-size graph-native traffic benchmarks—METRLA-20 and PEMSBAY-50—the learned filter produces sharper at-target ellipsoids than static-covariance and non-filter baselines [1]. At joint coverage of 0.910 and 0.904, widths reached 3.05 and 1.98, representing reductions of 23.6% and 40.5% versus a static-covariance baseline, and 8.4% and 13.9% versus the strongest at-target non-filter competitor [3]. An adaptive conformal inference wrap preserved at-target coverage and slightly tightened the METRLA result from 3.05 to 2.95; at full-graph scale on PEMSBAY-325, it restored at-target coverage from 0.878 to 0.899 [3]. Related work has explored conformal prediction for graph time-series forecasting. One study proposed graph-aware nonconforming scores where residuals are filtered through a graph convolutional operator, yielding ellipsoids whose volume shrinks exponentially with the filter coefficient and graph spectrum under a homophily assumption [4]. Another line of research introduced spectral graph conditional exchangeability, decomposing multivariate time series into low- and high-frequency components via graph wavelets and conformalizing high-frequency residual scores, providing a new paradigm for conformal prediction in graph-structured settings [5]. The filtered conformal ellipsoids paper extends this landscape by combining a recurrent filter with split-conformal calibration and providing theoretical coverage guarantees under dependence [1].