Estimating latent feature-feature interactions in large feature-rich graphs

Real-world complex networks describe connections between objects; in reality, those objects are often endowed with some kind of features. How does the presence or absence of such features interplay with the network link structure? Although the situation here described is truly ubiquitous, there is a limited body of research dealing with large graphs of this kind. Many previous works considered homophily as the only possible transmission mechanism translating node features into links. Other authors, instead, developed more sophisticated models, that are able to handle complex feature interactions, but are unfit to scale to very large networks. We expand on the MGJ model, where interactions between pairs of features can foster or discourage link formation. In this work, we will investigate how to estimate the latent feature-feature interactions in this model. We shall propose two solutions: the first one assumes feature independence and it is essentially based on Naive Bayes; the second one, which relaxes the independence assumption assumption, is based on perceptrons. In fact, we show it is possible to cast the model equation in order to see it as the prediction rule of a perceptron. We analyze how classical results for the perceptrons can be interpreted in this context; then, we define a fast and simple perceptron-like algorithm for this task, which can process $10^8$ links in minutes. We then compare these two techniques, first with synthetic datasets that follows our model, gaining evidence that the Naive independence assumptions are detrimental in practice. Secondly, we consider a real, large-scale citation network where each node (i.e., paper) can be described by different types of characteristics; there, our algorithm can assess how well each set of features can explain the links, and thus finding meaningful latent feature-feature interactions.