Reconstructing graph diffusion history from a single snapshot

Qiu, Ruizhong

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https://hdl.handle.net/2142/124242 Copy

Description

Title

Reconstructing graph diffusion history from a single snapshot

Author(s)

Qiu, Ruizhong

Issue Date

2024-04-09

Director of Research (if dissertation) or Advisor (if thesis)

Tong, Hanghang

Department of Study

Computer Science

Discipline

Computer Science

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

M.S.

Degree Level

Thesis

Keyword(s)

• Graph diffusion
• History reconstruction
• Markov chain Monte Carlo
• Graph neural network

Abstract

Diffusion on graphs is ubiquitous with numerous high-impact applications, ranging from the study of residential segregation in socioeconomics and activation cascading in neuroscience, to the modeling of disease contagion in epidemiology and malware spreading in cybersecurity. In these applications, complete diffusion histories play an essential role in terms of identifying dynamical patterns, reflecting on precaution actions, and forecasting intervention effects. Despite their importance, complete diffusion histories are rarely available and are highly challenging to reconstruct due to ill posedness, explosive search space, and scarcity of training data. To date, few methods exist for diffusion history reconstruction. They are exclusively based on the maximum likelihood estimation (MLE) formulation and require to know true diffusion parameters. In this thesis, we study an even harder problem, namely reconstructing Diffusion history from A single SnapsHot (DASH), where we seek to reconstruct the history from only the final snapshot without knowing true diffusion parameters. We start with theoretical analyses that reveal a fundamental limitation of the MLE formulation. We prove: (a) estimation error of diffusion parameters is unavoidable due to NP-hardness of diffusion parameter estimation, and (b) the MLE formulation is sensitive to estimation error of diffusion parameters. To overcome the inherent limitation of the MLE formulation, we propose a novel barycenter formulation: finding the barycenter of the posterior distribution of histories, which is provably stable against the estimation error of diffusion parameters. We further develop an effective solver named DIffusion hiTting Times with Optimal proposal (DITTO) by reducing the problem to estimating posterior expected hitting times via the Metropolis–Hastings Markov chain Monte Carlo method (M–H MCMC) and employing an unsupervised graph neural network to learn an optimal proposal to accelerate the convergence of M–H MCMC. We conduct extensive experiments to demonstrate the efficacy of the proposed method. Our code is available at https://github.com/q-rz/KDD23-DITTO.

Graduation Semester

2024-05

Type of Resource

Thesis

Copyright and License Information

Copyright 2024 Ruizhong Qiu

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