Decoupled Smoothing on Graphs

Graph smoothing methods are an extremely popular family of approaches for semi-supervised learning. The choice of graph used to represent relationships in these learning problems is often a more important decision than the particular algorithm or loss function used, yet this choice is less well-studied in the literature. In this work, we demonstrate that for social networks, the basic friendship graph itself may often not be the appropriate graph for predicting node attributes using graph smoothing. More specifically, standard graph smoothing is designed to harness the social phenomenon of homophily whereby individuals are similar to “the company they keep.” We present a decoupled approach to graph smoothing that decouples notions of “identity” and “preference,” resulting in an alternative social phenomenon of monophily whereby individuals are similar to “the company they're kept in,” as observed in recent empirical work. Our model results in a rigorous extension of the Gaussian Markov Random Field (GMRF) models that underlie graph smoothing, interpretable as smoothing on an appropriate auxiliary graph of weighted or unweighted two-hop relationships.