Convex Parameter Recovery for Interacting Marked Processes
This provides a more flexible modeling approach for event data analysis in domains like public safety, though it appears incremental relative to existing marked point process methods.
The authors tackled the problem of modeling multivariate discrete event data with categorical interacting marks by introducing marked Bernoulli processes that allow arbitrary influence shapes from historical events, locations, and categories. They developed constrained Least Squares and Maximum Likelihood estimation procedures using variational inequalities with monotone operators, demonstrating performance on synthetic examples and a real-world police dataset.
We introduce a new general modeling approach for multivariate discrete event data with categorical interacting marks, which we refer to as marked Bernoulli processes. In the proposed model, the probability of an event of a specific category to occur in a location may be influenced by past events at this and other locations. We do not restrict interactions to be positive or decaying over time as it is commonly adopted, allowing us to capture an arbitrary shape of influence from historical events, locations, and events of different categories. In our modeling, prior knowledge is incorporated by allowing general convex constraints on model parameters. We develop two parameter estimation procedures utilizing the constrained Least Squares (LS) and Maximum Likelihood (ML) estimation, which are solved using variational inequalities with monotone operators. We discuss different applications of our approach and illustrate the performance of proposed recovery routines on synthetic examples and a real-world police dataset.