Markov-modulated Marked Poisson Processes for Check-in Data

We develop continuous-time probabilistic models to study trajectory data consisting of times and locations of user 'check-ins'. We model the data as realizations of a marked point process, with intensity and mark-distribution modulated by a latent Markov jump process (MJP). We also include user-heterogeneity in our model by assigning each user a vector of 'preferred locations'. Our model extends latent Dirichlet allocation by dropping the bag-of-words assumption and operating in continuous time. We show how an appropriate choice of priors allows efficient posterior inference. Our experiments demonstrate the usefulness of our approach by comparing with various baselines on a variety of tasks.