# Topology-Aware Conformal Prediction for Stream Networks

arXiv: https://arxiv.org/abs/2503.04981 · HTML: https://mlsanity.com/paper/2503.04981/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 60 references that are in the map.
- First posted on arXiv 6 Mar 2025.

## Builds on (most cited first, 28 of 28)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2106.12931/) (2021)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [PyTorch Geometric Temporal: Spatiotemporal Signal Processing with Neural Machine Learning Models](https://mlsanity.com/paper/2104.07788/) (2021)
- [LargeST: A Benchmark Dataset for Large-Scale Traffic Forecasting](https://mlsanity.com/paper/2306.08259/) (2023)
- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Conformal prediction for time series](https://mlsanity.com/paper/2010.09107/) (2020)
- [Copula-based conformal prediction for Multi-Target Regression](https://mlsanity.com/paper/2101.12002/) (2021)
- [Quantifying Uncertainty in Deep Spatiotemporal Forecasting](https://mlsanity.com/paper/2105.11982/) (2021)
- [Conformal prediction for multi-dimensional time series by ellipsoidal sets](https://mlsanity.com/paper/2403.03850/) (2024)
- [Uncertainty Quantification of Sparse Travel Demand Prediction with Spatial-Temporal Graph Neural Networks](https://mlsanity.com/paper/2208.05908/) (2022)
- [Distribution Free Prediction Sets for Node Classification](https://mlsanity.com/paper/2211.14555/) (2022)
- [Uncertainty in Graph Neural Networks: A Survey](https://mlsanity.com/paper/2403.07185/) (2024)
- [Uncertainty Quantification for Traffic Forecasting: A Unified Approach](https://mlsanity.com/paper/2208.05875/) (2022)
- [Uncertainty Quantification with Generative Models](https://mlsanity.com/paper/1910.10046/) (2019)
- [Conformal Prediction for Network-Assisted Regression](https://mlsanity.com/paper/2302.10095/) (2023)
- [Non-Stationary Spatial Modeling](https://mlsanity.com/paper/2212.08043/) (2022)
- [Bellman Conformal Inference: Calibrating Prediction Intervals For Time Series](https://mlsanity.com/paper/2402.05203/) (2024)
- [A Hybrid Method for Traffic Flow Forecasting Using Multimodal Deep Learning](https://mlsanity.com/paper/1803.02099/) (2018)
- [Spatio-Temporal Point Processes with Attention for Traffic Congestion Event Modeling](https://mlsanity.com/paper/2005.08665/) (2020)
- [Uncertainty Quantification of Spatiotemporal Travel Demand with Probabilistic Graph Neural Networks](https://mlsanity.com/paper/2303.04040/) (2023)
- [Conformal Methods for Quantifying Uncertainty in Spatiotemporal Data: A Survey](https://mlsanity.com/paper/2209.03580/) (2022)
- [Conformal prediction intervals for the individual treatment effect](https://mlsanity.com/paper/2006.01474/) (2020)
- [Generative Conformal Prediction with Optimized Coverage Allocation](https://mlsanity.com/paper/2410.13735/) (2024)
- [Distribution-Free Prediction Bands for Multivariate Functional Time Series: an Application to the Italian Gas Market](https://mlsanity.com/paper/2107.00527/) (2021)

## Built on by (most cited first, 3 of 3)

- [Conformal-DRO: Distributionally Robust Optimization with Conformalized Ambiguity Set](https://mlsanity.com/paper/2609.11073/) (2026)
- [Filtered Conformal Ellipsoids for Graph-Native Time Series](https://mlsanity.com/paper/2606.17014/) (2026)
- [Tail-Aware Geometry Learning for Conformal Ellipsoids](https://mlsanity.com/paper/2609.27221/) (2026)

## Abstract (arXiv)

Stream networks, a unique class of spatiotemporal graphs, exhibit complex directional flow constraints and evolving dependencies, making uncertainty quantification a critical yet challenging task. Traditional conformal prediction methods struggle in this setting due to the need for joint predictions across multiple interdependent locations and the intricate spatio-temporal dependencies inherent in stream networks. Existing approaches either neglect dependencies, leading to overly conservative predictions, or rely solely on data-driven estimations, failing to capture the rich topological structure of the network. To address these challenges, we propose Spatio-Temporal Adaptive Conformal Inference (textttSTACI), a novel framework that integrates network topology and temporal dynamics into the conformal prediction framework. textttSTACI introduces a topology-aware nonconformity score that respects directional flow constraints and dynamically adjusts prediction sets to account for temporal distributional shifts. We provide theoretical guarantees on the validity of our approach and demonstrate its superior performance on both synthetic and real-world datasets. Our results show that textttSTACI effectively balances prediction efficiency and coverage, outperforming existing conformal prediction methods for stream networks.