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Abstract:
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Dynamic networks are ubiquitous in sociology, biology, epidemiology, and other fields. Dynamic latent space models (LSMs), which embed dynamic networks into a low-dimensional latent space, can uncover the structure and evolution of these networks. Long-standing issues with dynamic LSMs include only modeling positive semi-definite log-odds matrices, identifiability issues that make it impossible to assign time-varying importance to each latent dimension, and no rigorous method to select the latent space's dimension. These limitations can incur significant bias, which undermines the usefulness of these models. This work presents a new Bayesian latent space approach for dynamic networks that can model general symmetric log-odds matrices and assign time-varying importance to each latent dimension. In addition, we provide a prior distribution and posterior inference over the latent space's dimension. We also introduce a novel parameter expansion scheme that allows for efficient estimation with a Hamiltonian-within-Gibbs sampler. We demonstrate the model's ability to select an appropriate latent space dimension and provide meaningful insights by analyzing simulated and real networks.
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