# Relational Conformal Prediction for Correlated Time Series

arXiv: https://arxiv.org/abs/2502.09443 · HTML: https://mlsanity.com/paper/2502.09443/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 83 references that are in the map.
- First posted on arXiv 13 Feb 2025.

## Builds on (most cited first, 30 of 53)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1905.07953/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Stochastic Beams and Where to Find Them: The Gumbel-Top-k Trick for Sampling Sequences Without Replacement](https://mlsanity.com/paper/1903.06059/) (2019)
- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Deep Learning for Time Series Forecasting: Tutorial and Literature Survey](https://mlsanity.com/paper/2004.10240/) (2020)
- [A Gentle Introduction to Deep Learning for Graphs](https://mlsanity.com/paper/1912.12693/) (2019)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks](https://mlsanity.com/paper/2108.00298/) (2021)
- [Differentiable Graph Module (DGM) for Graph Convolutional Networks](https://mlsanity.com/paper/2002.04999/) (2020)
- [DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Models](https://mlsanity.com/paper/2301.13629/) (2023)
- [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)
- [Reparameterizable Subset Sampling via Continuous Relaxations](https://mlsanity.com/paper/1901.10517/) (2019)

## Built on by (most cited first, 11 of 11)

- [ResCP: Reservoir Conformal Prediction for Time Series Forecasting](https://mlsanity.com/paper/2510.05060/) (2025)
- [Do Time Series Foundation Model Benchmarks Hide Regime-Dependent Failures? Evidence from Traffic Speed Forecasting](https://mlsanity.com/paper/2606.18367/) (2026)
- [Rethinking the Role of LLMs in Time Series Forecasting](https://mlsanity.com/paper/2602.14744/) (2026)
- [Zono-Conformal Prediction: Zonotope-Based Uncertainty Quantification for Regression and Classification Tasks](https://mlsanity.com/paper/2508.11025/) (2025)
- [MoGU: Mixture-of-Gaussians with Uncertainty-based Gating for Time Series Forecasting](https://mlsanity.com/paper/2510.07459/) (2025)
- [Retrieval-Corrected Conformal Prediction for Time Series](https://mlsanity.com/paper/2608.10553/) (2026)
- [Virtual Smart Metering in District Heating Networks via Heterogeneous Spatial-Temporal Graph Neural Networks](https://mlsanity.com/paper/2604.10166/) (2026)
- [Delving into Non-Exchangeability for Conformal Prediction in Graph-Structured Multivariate Time Series](https://mlsanity.com/paper/2605.04957/) (2026)
- [Multi-Variable Conformal Prediction: Optimizing Prediction Sets without Data Splitting](https://mlsanity.com/paper/2605.12341/) (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)

## Abstract (arXiv)

We address the problem of uncertainty quantification in time series forecasting by exploiting observations at correlated sequences. Relational deep learning methods leveraging graph representations are among the most effective tools for obtaining point estimates from spatiotemporal data and correlated time series. However, the problem of exploiting relational structures to estimate the uncertainty of such predictions has been largely overlooked in the same context. To this end, we propose a novel distribution-free approach based on the conformal prediction framework and quantile regression. Despite the recent applications of conformal prediction to sequential data, existing methods operate independently on each target time series and do not account for relationships among them when constructing the prediction interval. We fill this void by introducing a novel conformal prediction method based on graph deep learning operators. Our approach, named Conformal Relational Prediction (CoRel), does not require the relational structure (graph) to be known a priori and can be applied on top of any pre-trained predictor. Additionally, CoRel includes an adaptive component to handle non-exchangeable data and changes in the input time series. Our approach provides accurate coverage and achieves state-of-the-art uncertainty quantification in relevant benchmarks.