Inferring high-dimensional poisson autoregressive models

Eric C. Hall, Garvesh Raskutti, Rebecca Willett

Abstract: Consider observing a series of events associated with a group of interacting nodes in a network, where the interactions among those nodes govern the likelihood of future events. Such data are common in spike trains recorded from biological neural networks, interactions within a social network, and pricing changes within financial networks. Vector autoregressive point processes accurately model these settings and are widely used in practice. This paper addresses the inference of the network structure and autoregressive parameters from such data. A sparsity-regularized maximum likelihood estimator is proposed for a Poisson autoregressive process. While sparsity-regularization is well-studied in the statistics and machine learning communities, common assumptions from that literature are difficult to verify here because of correlations and heteroscedasticity inherent in the problem. Novel performance guarantees characterize how much data must be collected to ensure reliable inference depending on the size and sparsity of the autoregressive parameters, and these bounds are supported by several simulation studies.