# Conformal Inference for Time Series over Graphs

arXiv: https://arxiv.org/abs/2510.11049 · HTML: https://mlsanity.com/paper/2510.11049/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 15 references that are in the map.
- First posted on arXiv 13 Oct 2025.

## Builds on (most cited first, 9 of 9)

- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Structure-Aware Transformer for Graph Representation Learning](https://mlsanity.com/paper/2202.03036/) (2022)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [Conformal prediction for time series](https://mlsanity.com/paper/2010.09107/) (2020)
- [Conformal prediction for multi-dimensional time series by ellipsoidal sets](https://mlsanity.com/paper/2403.03850/) (2024)
- [Inductive Conformal Martingales for Change-Point Detection](https://mlsanity.com/paper/1706.03415/) (2017)

## Built on by (most cited first, 5 of 5)

- [Conflict Forecasting via Conformal Prediction for Markov Processes](https://mlsanity.com/paper/2604.25139/) (2026)
- [Online Conformal Prediction with Corrupted Feedback](https://mlsanity.com/paper/2605.20515/) (2026)
- [Filtered Conformal Ellipsoids for Graph-Native Time Series](https://mlsanity.com/paper/2606.17014/) (2026)
- [In-Context Residual Calibration for Uncertainty Quantification of Energy Time Series over Graphs](https://mlsanity.com/paper/2606.31804/) (2026)
- [Tail-Aware Geometry Learning for Conformal Ellipsoids](https://mlsanity.com/paper/2609.27221/) (2026)

## Abstract (arXiv)

Trustworthy decision making in networked, dynamic environments calls for innovative uncertainty quantification substrates in predictive models for graph time series. Existing conformal prediction (CP) methods have been applied separately to multivariate time series and static graphs, but they either ignore the underlying graph topology or neglect temporal dynamics. To bridge this gap, here we develop a CP-based sequential prediction region framework tailored for graph time series. A key technical innovation is to leverage the graph structure and thus capture pairwise dependencies across nodes, while providing user-specified coverage guarantees on the predictive outcomes. We formally establish that our scheme yields an exponential shrinkage in the volume of the ellipsoidal prediction set relative to its graph-agnostic counterpart. Using real-world datasets, we demonstrate that the novel uncertainty quantification framework maintains desired empirical coverage while achieving markedly smaller (up to 80% reduction) prediction regions than existing approaches.