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Abstract:
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Latent space network models [Hoff et al. 2002] and their variations are some of the most ubiquitous in statistical network analysis. Traditionally selecting the latent space geometry, whether spherical, Euclidean or hyperbolic has been a modelling decision, rather than a parameter which can be learned from the network itself. Recently, Lubold et al. [2020] developed a method for estimating the curvature of the latent space. In this paper, we extend the previous results and develop a novel estimator for the curvature which is both, local in scale, and asymptotically normal. The advantages of this estimator allow for the simple construction of downstream statistical tests, which we highlight in the examples of 1) testing for constant curvature in a single network, 2) testing for a change in curvature across views in a multiplex network, and 3) testing for a change in curvature in sequential network data. We then apply these tests to the Unified Host and Network Dataset from Los Alamos National Laboratories to investigate changes in curvature over time.
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