# Conformal Prediction for Multi-Source Detection on a Network

arXiv: https://arxiv.org/abs/2511.08867 · HTML: https://mlsanity.com/paper/2511.08867/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 12 Nov 2025.

## Builds on (most cited first, 16 of 16)

- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Improved Online Conformal Prediction via Strongly Adaptive Online Learning](https://mlsanity.com/paper/2302.07869/) (2023)
- [Online conformal prediction with decaying step sizes](https://mlsanity.com/paper/2402.01139/) (2024)
- [Finding Patient Zero: Learning Contagion Source with Graph Neural Networks](https://mlsanity.com/paper/2006.11913/) (2020)
- [Conformal Inductive Graph Neural Networks](https://mlsanity.com/paper/2407.09173/) (2024)
- [Multi-label Classification under Uncertainty: A Tree-based Conformal Prediction Approach](https://mlsanity.com/paper/2404.19472/) (2024)
- [Diffusion Source Identification on Networks with Statistical Confidence](https://mlsanity.com/paper/2106.04800/) (2021)
- [Well-calibrated Confidence Measures for Multi-label Text Classification with a Large Number of Labels](https://mlsanity.com/paper/2312.09304/) (2023)
- [A Robust Information Source Estimator with Sparse Observations](https://mlsanity.com/paper/1309.4846/) (2013)
- [On the Universality of Jordan Centers for Estimating Infection Sources in Tree Networks](https://mlsanity.com/paper/1411.2370/) (2014)
- [On the Properties of Gromov Matrices and their Applications in Network Inference](https://mlsanity.com/paper/1810.05333/) (2018)
- [Estimating Infection Sources in Networks Using Partial Timestamps](https://mlsanity.com/paper/1711.01537/) (2017)

## Abstract (arXiv)

Detecting the origin of information or infection spread in networks is a fundamental challenge with applications in misinformation tracking, epidemiology, and beyond. We study the multi-source detection problem: given snapshot observations of node infection status on a graph, estimate the set of source nodes that initiated the propagation. Existing methods either lack statistical guarantees or are limited to specific diffusion models and assumptions. We propose a novel conformal prediction framework that provides statistically valid recall guarantees for source set detection, independent of the underlying diffusion process or data distribution. Our approach introduces principled score functions to quantify the alignment between predicted probabilities and true sources, and leverages a calibration set to construct prediction sets with user-specified recall and coverage levels. The method is applicable to both single- and multi-source scenarios, supports general network diffusion dynamics, and is computationally efficient for large graphs. Empirical results demonstrate that our method achieves rigorous coverage with competitive accuracy, outperforming existing baselines in both reliability and scalability.The code is available online.