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Robust Estimation of Self-Exciting Point Process Models with Application to Neuronal Modeling



We consider the problem of estimating discrete self- exciting point process models from limited binary observations, where the history of the process serves as the covariate. We analyze the performance of two classes of estimators: l1-regularized maximum likelihood and greedy estimation for a discrete version of the Hawkes process and characterize the sampling tradeoffs required for stable recovery in the non-asymptotic regime. Our results extend those of compressed sensing for linear and generalized linear models with i.i.d. covariates to point processes with highly inter-dependent covariates. We further provide simulation studies as well as application to real spiking data from mouse’s lateral geniculate nucleus and ferret’s retinal ganglion cells which agree with our theoretical predictions.

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