Multiple-Source Localization from a Single-Snapshot Observation Using Graph Bayesian Optimization

TL;DR

This work tackles multi-source localization from a single snapshot in networks by introducing BOSouL, a simulation-based Bayesian optimization framework that can accommodate arbitrary diffusion models. BOSouL builds a Gaussian process surrogate using a graph spectral kernel to model the relationship between candidate source sets and observed diffusion outcomes, and it guides data acquisition with graph stratified sampling and an expected-improvement criterion. The paper proves that the proposed graph spectral kernel is a valid Mercer kernel, analyzes the algorithm’s time complexity, and demonstrates robust performance across real and synthetic graphs under various diffusion models, with notable accuracy gains over strong baselines and acceptable runtimes. The approach offers a flexible, model-agnostic tool for diffusion-source localization with practical impact for epidemiology, security, and network resilience, and the authors provide a public code release.

Abstract

Due to the significance of its various applications, source localization has garnered considerable attention as one of the most important means to confront diffusion hazards. Multi-source localization from a single-snapshot observation is especially relevant due to its prevalence. However, the inherent complexities of this problem, such as limited information, interactions among sources, and dependence on diffusion models, pose challenges to resolution. Current methods typically utilize heuristics and greedy selection, and they are usually bonded with one diffusion model. Consequently, their effectiveness is constrained. To address these limitations, we propose a simulation-based method termed BOSouL. Bayesian optimization (BO) is adopted to approximate the results for its sample efficiency. A surrogate function models uncertainty from the limited information. It takes sets of nodes as the input instead of individual nodes. BOSouL can incorporate any diffusion model in the data acquisition process through simulations. Empirical studies demonstrate that its performance is robust across graph structures and diffusion models. The code is available at https://github.com/XGraph-Team/BOSouL.

Figures (5)

• Figure 1: The challenges faced by heuristic methods: (a) Sources and spreads have many-to-many relationships. (b) Greedy algorithms result in sub-optimal solutions (top). (c) Different diffusion models (SI at the top and SIR at the bottom) affect source localization results.
• Figure 2: Illustration of the proposed ${\textsf{BOSouL}}$. Based on their graph Fourier representations, all possible candidates for source node sets are clustered in the bottom half of this figure. As training sets for GP, the model samples instances from each group utilizing GSS. In the upper half, one optimal instance is chosen by the surrogate GP (Max), and its likelihood of being a genuine source is determined through simulation. Sampling and training will be performed iteratively, and in each iteration, the GP model will be updated from a prior to a posterior (for example, from 1 to 2 on the upper left).
• Figure 3: The distance toward the true source set with SIR.
• Figure 4: The distance toward the true source set with SI.
• Figure 5: Runtime analysis on SW graph.

Theorems & Definitions (5)

• Definition 1: Single-snapshot Multi-Source Localization
• Theorem
• proof
• Theorem
• proof