Network data, capturing the connections or interactions among subjects of interest, are widely used across numerous scientific disciplines. Recent years have seen a significant increase in time-varying network data, which record not only the number of interactions but also the precise timestamps when these events occur. These data call for novel analytical developments that specifically leverage the event time information.
In this thesis, we propose frameworks for analyzing longitudinal/panel network data and continuous time network data. For the analysis of longitudinal network data, we introduce a semiparametric latent space model. The model consists of a static latent space component and a time-varying node-specific baseline component. We develop a semiparametric efficient score equation for the latent space parameter. Estimation is accomplished through a one-step update estimator and a suitably penalized maximum likelihood estimator. We derive oracle error bounds for both estimators and address identifiability concerns from a quotient manifold perspective.
For analyzing continuous time network data, we introduce a Cox-type counting process latent space model. To accomodate the event history observations, each edge is modeled as a counting process, with intensity comprising three components: a time-dependent baseline function, an individual-level degree heterogeneity parameter, and a low-rank embedding for the interaction effects. A nuclear-norm penalized likelihood estimator is developed, and its oracle error bounds are established. Additionally, we discuss a several ongoing directions for this work.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/p6f1-ny22 |
| Date | January 2024 |
| Creators | Sun, Jiajin |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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