  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.
