B0951
Title: Using Hawkes processes to model sparse event networks
Authors: Alexander Kreiss - Leipzig University (Germany) [presenting]
Enno Mammen - Heidelberg University (Germany)
Wolfgang Polonik - University of California at Davis (United States)
Abstract: Consider the example of the social media setting in which the users (the actors) can cast certain events. These events are observed by the other users who then adjust their behavior, e.g., they cast an event themselves. Due to several mechanisms, the actors pay usually not the same amount of attention to all other actors. Examples of such mechanisms are: some sort of friendship structures selecting which events are visible at all to the other users, but even though users are exposed to other events they might simply ignore them due to time constraints. The superposition of all these effects can be seen as a weighted and directed attention network (an edge from one user to another means that the first user reacts to events cast by the second user). If the actors are humans, it is plausible that they have time constraints, and hence we suppose that such networks are sparse. A model for this type of data is considered based on Hawkes processes. The mutual excitation kernels of these depend on the attention network and additionally observed covariates. The aim is to estimate the network and the influence of the covariates. While it is supposed that the covariates are low dimensional, the size of the network is allowed to grow. By using the LASSO type, penalized least squares model fitting sparsity is addressed. The choice of the least squares criterion (as opposed to the likelihood) ensures that the problem can be reformulated as a standard linear model with LASSO constraints.
