Network estimation via poisson autoregressive models

Multivariate Poisson autoregressive models are a common way of capturing self-exciting point processes, where cascading series of events from nodes in a network either stimulate or inhibit events from other nodes. These models can be used to learn the structure of social or biological neural networks. An important problem associated with these multivariate network models is determining how different nodes influence each other. This problem presents a number of technical challenges since the number of nodes is typically large relative to the number of observed events. This paper addresses these challenges and provides learning rates for a class of multivariate self-exciting Poisson autoregressive models. Importantly, the derived learning rates apply in the high-dimensional setting when our network is sparse. We also provide a real data example to support our methodology and main results.