Scaling Choice Models of Relational Social Data

Abstract

Many prediction problems on social networks, from recommendations to anomaly detection, can be approached by modeling network data as a sequence of relational events and then leveraging the resulting model for prediction. Conditional logit models of discrete choice are a natural approach to modeling relational events as "choices" in a framework that envelops and extends many long-studied models of network formation. The conditional logit model is simplistic, but it is particularly attractive because it allows for efficient consistent likelihood maximization via negative sampling, something that isn't true for mixed logit and many other richer models. The value of negative sampling is particularly pronounced because choice sets in relational data are often enormous. Given the importance of negative sampling, in this work we introduce a model simplification technique for mixed logit models that we call "de-mixing", whereby standard mixture models of network formation---particularly models that mix local and global link formation---are reformulated to operate their modes over disjoint choice sets. This reformulation reduces mixed logit models to conditional logit models, opening the door to negative sampling while also circumventing other standard challenges with maximizing mixture model likelihoods. To further improve scalability, we also study importance sampling for more efficiently selecting negative samples, finding that it can greatly speed up inference in both standard and de-mixed models. Together, these steps make it possible to much more realistically model network formation in very large graphs. We illustrate the relative gains of our improvements on synthetic datasets with known ground truth as well as a large-scale dataset of public transactions on the Venmo platform.