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1. Inferring Dynamic Networks from Marginals with Iterative Proportional Fitting

   Chang, Serina; Koehler, Frederic; Qu, Zhaonan; Leskovec, Jure; Ugander, Johan (May 2024, Proceedings of Machine Learning Research)

   A common network inference problem, arising from real-world data constraints, is how to infer a dynamic network from its time-aggregated adjacency matrix and time-varying marginals (i.e., row and column sums). Prior approaches to this problem have repurposed the classic iterative proportional fitting (IPF) procedure, also known as Sinkhorn’s algorithm, with promising empirical results. However, the statistical foundation for using IPF has not been well understood: under what settings does IPF provide principled estimation of a dynamic network from its marginals, and how well does it estimate the network? In this work, we establish such a setting, by identifying a generative network model whose maximum likelihood estimates are recovered by IPF. Our model both reveals implicit assumptions on the use of IPF in such settings and enables new analyses, such as structure-dependent error bounds on IPF’s parameter estimates. When IPF fails to converge on sparse network data, we introduce a principled algorithm that guarantees IPF converges under minimal changes to the network structure. Finally, we conduct experiments with synthetic and real-world data, which demonstrate the practical value of our theoretical and algorithmic contributions. 

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2. Inferring Dynamic Networks from Marginals with Iterative Proportional Fitting

   Chang, Serina; Koehler, Frederic; Qu, Zhaonan; Leskovec, Jure; Ugander, Johan (May 2024, Proceedings of Machine Learning Research)

   A common network inference problem, arising from real-world data constraints, is how to infer a dynamic network from its time-aggregated adjacency matrix and time-varying marginals (i.e., row and column sums). Prior approaches to this problem have repurposed the classic iterative proportional fitting (IPF) procedure, also known as Sinkhorn’s algorithm, with promising empirical results. However, the statistical foundation for using IPF has not been well understood: under what settings does IPF provide principled estimation of a dynamic network from its marginals, and how well does it estimate the network? In this work, we establish such a setting, by identifying a generative network model whose maximum likelihood estimates are recovered by IPF. Our model both reveals implicit assumptions on the use of IPF in such settings and enables new analyses, such as structure-dependent error bounds on IPF’s parameter estimates. When IPF fails to converge on sparse network data, we introduce a principled algorithm that guarantees IPF converges under minimal changes to the network structure. Finally, we conduct experiments with synthetic and real-world data, which demonstrate the practical value of our theoretical and algorithmic contributions. 

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3. Learning Graph Structure from Convolutional Mixtures

   Wasserman, Max; Sihag, Saurabh; Mateos, Gonzalo; Ribeiro, Alejandro (June 2023, Transactions on machine learning research)

   Machine learning frameworks such as graph neural networks typically rely on a given, fixed graph to exploit relational inductive biases and thus effectively learn from network data. However, when said graphs are (partially) unobserved, noisy, or dynamic, the problem of inferring graph structure from data becomes relevant. In this paper, we postulate a graph convolutional relationship between the observed and latent graphs, and formulate the graph structure learning task as a network inverse (deconvolution) problem. In lieu of eigendecomposition-based spectral methods or iterative optimization solutions, we unroll and truncate proximal gradient iterations to arrive at a parameterized neural network architecture that we call a Graph Deconvolution Network (GDN). GDNs can learn a distribution of graphs in a supervised fashion, perform link prediction or edge-weight regression tasks by adapting the loss function, and they are inherently inductive as well as node permutation equivariant. We corroborate GDN’s superior graph learning performance and its generalization to larger graphs using synthetic data in supervised settings. Moreover, we demonstrate the robustness and representation power of GDNs on real world neuroimaging and social network datasets. 

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4. On Algorithmic Decision Procedures in Emergency Response Systems in Smart and Connected Communities

   Pettet, Geoffrey; Mukhopadhyay, Ayan; Kochenderfer, Mykel; Vorobeychik, Yevgeniy; Dubey, Abhishek (January 2020, International Conference on Autonomous Agents and Multiagent Systems (AAMAS))

   Emergency Response Management (ERM) is a critical problem faced by communities across the globe. Despite this, it is common for ERM systems to follow myopic decision policies in the real world. Principled approaches to aid ERM decision-making under uncertainty have been explored but have failed to be accepted into real systems. We identify a key issue impeding their adoption — algorithmic approaches to emergency response focus on reactive, post-incident dispatching actions, i.e. optimally dispatching a responder after incidents occur. However, the critical nature of emergency response dictates that when an incident occurs, first responders always dispatch the closest available responder to the incident. We argue that the crucial period of planning for ERM systems is not post-incident, but between incidents. This is not a trivial planning problem — a major challenge with dynamically balancing the spatial distribution of responders is the complexity of the problem. An orthogonal problem in ERM systems is planning under limited communication, which is particularly important in disaster scenarios that affect communication networks. We address both problems by proposing two partially decentralized multi-agent planning algorithms that utilize heuristics and exploit the structure of the dispatch problem. We evaluate our proposed approach using real-world data, and find that in several contexts, dynamic re-balancing the spatial distribution of emergency responders reduces both the average response time as well as its variance. 

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5. On Algorithmic Decision Procedures in Emergency Response Systems in Smart and Connected Communities

   Pettet, Geoffrey; Mukhopadhyay, Ayan; Kochenderfer, Mykel; Vorobeychik, Yevgeniy; Dubey, Abhishek (January 2020, roceedings of the 19th International Conference on Autonomous Agents and MultiAgent Systems)

   Emergency Response Management (ERM) is a critical problem faced by communities across the globe. Despite this, it is common for ERM systems to follow myopic decision policies in the real world. Principled approaches to aid ERM decision-making under uncertainty have been explored but have failed to be accepted into real systems. We identify a key issue impeding their adoption --- algorithmic approaches to emergency response focus on reactive, post-incident dispatching actions, i.e. optimally dispatching a responder after incidents occur. However, the critical nature of emergency response dictates that when an incident occurs, first responders always dispatch the closest available responder to the incident. We argue that the crucial period of planning for ERM systems is not post-incident, but between incidents. This is not a trivial planning problem --- a major challenge with dynamically balancing the spatial distribution of responders is the complexity of the problem. An orthogonal problem in ERM systems is planning under limited communication, which is particularly important in disaster scenarios that affect communication networks. We address both problems by proposing two partially decentralized multi-agent planning algorithms that utilize heuristics and exploit the structure of the dispatch problem. We evaluate our proposed approach using real-world data, and find that in several contexts, dynamic re-balancing the spatial distribution of emergency responders reduces both the average response time as well as its variance. 

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