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Abstract:
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User profiles in social networks are notoriously incomplete due to self-reporting; predicting or imputing these missing values is often of paramount importance. While missing value imputation has been widely studied in the context of standard data matrices, the network with node attributes case remains fairly unexplored. In particular, using all available information, observed node attributes and edges, should improve on using only the observed attributes, provided some association between attributes and edges. We propose a novel imputation method based on a joint latent space model that allows information between the network adjacency matrix and node attributes to be shared. Additionally, we propose an extension to non-ignorable missing values by directly modeling the missingness process. Using variational inference, we obtain approximate posteriors for the latent variables enabling predictive distributions for the missing values and further allowing assessment of missingness patterns. Numerical experiments, on both simulated and real-world networks, show that our proposed method improves on multiple imputation using only the nodes attributes.
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