1. Models for dynamic networks with metadata
- Author
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Fitzgerald, John, O'Clery, Neave, and Grindrod, Peter
- Subjects
Graphical modeling (Statistics) ,Graph algorithms ,Mathematics ,Probability learning ,Cluster analysis ,Machine learning ,Open source software - Abstract
There is increasing understanding that many complex systems of interest - everything from the global economy, to social group dynamics, to biochemical processes in the brain - require holistic modelling, rather than the consideration of units of the population in isolation. Network science techniques, which commence by viewing the system as a set of vertices or nodes (the units of the population, e.g. individual people) and edges (the relationships between them, e.g. friendship), are one popular approach to do so. Naturally, such complex systems express a wide array of important properties that we ought to account for when modelling them, beyond simply the presence or absence of a particular relationship. Most pertinently for this work, they evolve over time - i.e. they are 'dynamic' - and the units of the population may have distinct properties, or attributes, which further differentiate them from each other. We define any such extra information we might possess outside of the simple node/edge paradigm to be 'metadata'. Despite the potential utility of such metadata, it is only quite recently that methods have begun to jointly model both network and metadata together. In this thesis, we provide a new class of models that do so - specifically, with the purpose of finding groups in networks that change over time. We describe distinct versions of this class of models that allow the networks to be weighted and directed, as well as avoid the potential issue of placing nodes with similar degrees in the same group. In addition to elaborating such models, we derive novel requirements for the efficient detectability of groups given the presence of metadata - and in the process explain why a recent paper which claims to do the same for a similar static model is flawed. The inference method we leverage to investigate detectability is also highly scalable, and we further accelerate the process by proposing both a 'greedy' scheme, and a recursive procedure that effectively provides a top-down hierarchy of the network groups. We conclude by using our models as one component of a larger method, that provides an entirely novel means of estimating the influence of an author. We use a causal framing of the problem that to our knowledge has not previously been explored in this context, and depends upon recent ideas from the causal inference literature.
- Published
- 2022