FM-Hawkes: A Hawkes Process Based Approach for Modeling Online Activity Correlations

Understanding and predicting user behavior on online platforms has proved to be of significant value, with applications spanning from targeted advertising, political campaigning, anomaly detection to user self-monitoring. With the growing functionality and flexibility of online platforms, users can now accomplish a variety of tasks online. This advancement has rendered many previous works that focus on modeling a single type of activity obsolete. In this work, we target this new problem by modeling the interplay between the time series of different types of activities and apply our model to predict future user behavior. Our model, FM-Hawkes, stands for Fourier-based kernel multi-dimensional Hawkes process. Specifically, we model the multiple activity time series as a multi-dimensional Hawkes process. The correlations between different types of activities are then captured by the influence factor. As for the temporal triggering kernel, we observe that the intensity function consists of numerous kernel functions with time shift. Thus, we employ a Fourier transformation based non-parametric estimation. Our model is not bound to any particular platform and explicitly interprets the causal relationship between actions. By applying our model to real-life datasets, we confirm that the mutual excitation effect between different activities prevails among users. Prediction results show our superiority over models that do not consider action types and flexible kernels