Temporal Point Process Graphical Models

TL;DR

This paper introduces a novel class of temporal point process graphical models that capture nonlinear temporal dependencies in multivariate event streams on graphs, with efficient estimation procedures and theoretical error bounds.

Contribution

It proposes a new modeling framework for multivariate event data with nonlinear dependencies, including estimation algorithms and error analysis.

Findings

Effective in high-dimensional settings

Accurate parameter estimation demonstrated

Performs well on simulated and real data

Abstract

Many real-world objects can be modeled as a stream of events on the nodes of a graph. In this paper, we propose a class of graphical event models named temporal point process graphical models for representing the temporal dependencies among different components of a multivariate point process. In our model, the intensity of an event stream can depend on the historical events in a nonlinear way. We provide a procedure that allows us to estimate the parameters in the model with a convex loss function in the high-dimensional setting. For the approximation error introduced during the implementation, we also establish the error bound for our estimators. We demonstrate the performance of our method with extensive simulations and a spike train data set.