Change Point Detection in Dynamic Graphs with Decoder-only Latent Space Model
Abstract: This manuscript studies the unsupervised change point detection problem in time series of graphs using a decoder-only latent space model. The proposed framework consists of learnable prior distributions for low-dimensional graph representations and of a decoder that bridges the observed graphs and latent representations. The prior distributions of the latent spaces are learned from the observed data as empirical Bayes to assist change point detection. Specifically, the model parameters are estimated via maximum approximate likelihood, with a Group Fused Lasso regularization imposed on the prior parameters. The augmented Lagrangian is solved via Alternating Direction Method of Multipliers, and Langevin Dynamics are recruited for posterior inference. Simulation studies show good performance of the latent space model in supporting change point detection and real data experiments yield change points that align with significant events.
Submission Length: Long submission (more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=FVygyCbzon
Changes Since Last Submission: Dear Action Editors,
We sincerely appreciate the detailed feedback and constructive comments provided during previous review process for our manuscript titled "Generative Model for Change Point Detection in Dynamic Graphs" (Submission Number: 2904). The manuscript was previously handled by \textbf{Dr. Sinead Williamson} and \textbf{recommended for resubmission} after major revision. Based on the insightful review comments, we have undertaken substantial revisions to address all concerns raised and improve the quality of our work. Below, we outline the significant changes made in this revised submission:
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1. \textbf{[Real Data Experiments]} To qualitatively compare the detected change points across different methods, we fit Random Dot Product Graph models to the networks between consecutive detected change points, and we evaluate the log-likelihood of out-of-sample graphs that are excluded during fitting. A higher log-likelihood indicates that the detected change points segment the entire time span in a way that better captures the unchanged patterns within each interval. Our method yields the highest log-likelihood for out-of-sample graphs, and we provide justification for why some of the detected change points from competitor methods are unreasonable and unrealistic. Specifically, we now add Table 5 on Page 17 and Table 7 on Page 18.
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2. \textbf{[Simulation Study]} To evaluate the fidelity of generated graphs and the model's goodness of fit, we compare the degree distributions between the generated graphs and ground truth. Specifically, we learn a decoder with data that excludes graphs at particular time points, and we use the learned decoder to generate graphs at the removed time points. If the degree distributions are similar, it indicates that the graph decoder effectively captures the underlying structures, and the generated graphs closely resemble the ground truth. For our simulation studies, the degree distributions of the generated graphs align well with those of the originally simulated graphs. Specifically, we added Figures 5, 6, and 7 on Pages 14-15.
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3. \textbf{[Node level representation]} We compare our framework, which focuses on graph-level representation, to another change point detection method that focuses on node-level representation. The references, Larroca et al (2021), Marenco et al (2022) and Gong et al (2023) that are suggested by the AE, focus on weighed networks and online detection. Also, their codes are not publicly available. Instead, we compare with the CPDrdpg method (Madrid Padilla et al, 2022), which is the foundation of the references and focuses on offline change point detection for binary networks. Our method outperforms the competitors, demonstrating the effectiveness of using graph level representation to detect structural changes. Table 1 on Page 10, Table 2 on Page 12, and Table 3 on Page 13 show the associated results.
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4. We have updated the complexity of the algorithm on Page 26, and the url of codes will appear in the manuscript once anonymity is no longer required.
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We hope the revised manuscript now meets the expectations of TMLR and adequately addresses all concerns. We remain open to any further suggestions or modifications to improve the work further. Thank you for considering our resubmission.
Sincerely,
Authors of Manuscript 2904
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Reference:
1. Federico Larroca, Paola Bermolen, Marcelo Fiori, and Gonzalo Mateos. Change point detection in weighted and directed random dot product graphs. In 2021 29th European Signal Processing Conference, 2021.
2. Bernardo Marenco, Paola Bermolen, Marcelo Fiori, Federico Larroca, and Gonzalo Mateos. Online change point detection for weighted and directed random dot product graphs. IEEE Transactions on Signal and Information Processing over Networks, 2022.
3. Yongshun Gong, Xue Dong, Jian Zhang, and Meng Chen. Latent evolution model for change point detection
in time-varying networks. Information Sciences, 2023.
4. Oscar Hernan Madrid Padilla, Yi Yu, and Carey E Priebe. Change point localization in dependent dynamic nonparametric random dot product graphs. The Journal of Machine Learning Research, 2022.
Video: https://youtu.be/s4IFIuK-B5k
Code: https://github.com/allenkei/CPD_generative
Supplementary Material: zip
Assigned Action Editor: ~Francisco_J._R._Ruiz1
Submission Number: 4021
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