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Abstract:
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Statistical network modeling is powerful for understanding the underlying formation mechanism and characteristics of complex networks. However, statistical models for signed networks have been largely unexplored. In signed networks, there exist both positive and negative edges, which are commonly seen in real-world scenarios. The positive and negative edges in signed networks present unique structural patterns, which poses challenges for statistical modeling. In this work, we introduce a statistically principled latent space approach for modeling signed networks and accommodating the well-known balance property. The proposed approach treats both edges and their signs as random, and characterizes the balance property with a novel and natural notion of population-level balance. This approach guides us to build a series of balanced inner-product models. We develop scalable algorithms to estimate the latent variables and establish the non-asymptotic error rates, which are further verified through simulation studies. We also apply the proposed approach to a real-world signed network, which provides an informative and interpretable model-based visualization of international relations.
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