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Learning the latent network structure from large scale multivariate pointprocess data is an important task in a wide range of scientific and businessapplications. For instance, we might wish to estimate the neuronal functionalconnectivity network based on spiking times recorded from a collection ofneurons. To characterize the complex processes underlying the observed data, wepropose a new and flexible class of nonstationary Hawkes processes that allowboth excitatory and inhibitory effects. We estimate the latent networkstructure using an efficient sparse least squares estimation approach. Using athinning representation, we establish concentration inequalities for the firstand second order statistics of the proposed Hawkes process. Such theoreticalresults enable us to establish the non-asymptotic error bound and the selectionconsistency of the estimated parameters. Furthermore, we describe a leastsquares loss based statistic for testing if the background intensity isconstant in time. We demonstrate the efficacy of our proposed method throughsimulation studies and an application to a neuron spike train data set.

Latent Network Structure Learning from High Dimensional Multivariate Point Processes