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Content-based Modeling of Reciprocal Relationships using Hawkes and Gaussian Processes

There has been growing interest in inferring implicit social structures using interaction data. This approach is motivated by the fact that entities organize themselves into groups having frequent interactions between each other. Unlike previous approaches that focused on subjectively declared relationships, the idea is to exploit the actual evidence at hand to reach conclusions about group formations, resulting in more objective data-driven inferences. To this end, [5] have employed Hawkes processes, and proposed a Hawkes IRM model to infer social structures from interaction data. A major factor that encourages the use of Hawkes processes is the capability to model reciprocity in the interaction between social entities. However, reciprocation is dynamically conditioned upon two key factors: the significance of each message sent by the sender, and the receptivity to each message received by the receiver. In the model proposed by [5], reciprocity is not affected by either of these factors, since the content of each message is not taken into account. In this paper, we extend the work of [5] by introducing Gaussian processes (GPs) into the Hawkes IRM model: based on the content of each message, GPs are used to model the message significance as well as receptivity. This allows us to more accurately capture the interactions among entities. The application of GPs also allows us to flexibly model the rates of reciprocal activities between two entities, allowing asymmetry in reciprocity to be captured more accurately. This leads to better cluster detection capability. Our model outperforms previous Hawkes and Poisson process-based models at predicting verbal, email, and citation activities.