Robust Estimation of Self-Exciting Generalized Linear Models with Application to Neuronal Modeling
This work addresses robust estimation for neuronal modeling, representing an incremental extension of compressed sensing methods to dependent covariate settings.
The paper tackles the problem of estimating self-exciting generalized linear models from limited binary observations, analyzing ℓ₁-regularized maximum likelihood and greedy estimators to characterize sampling tradeoffs for stable recovery in non-asymptotic regimes. It extends compressed sensing results to models with interdependent covariates and validates findings with simulations and real neuronal spiking data.
We consider the problem of estimating self-exciting generalized linear models from limited binary observations, where the history of the process serves as the covariate. We analyze the performance of two classes of estimators, namely the $\ell_1$-regularized maximum likelihood and greedy estimators, for a canonical self-exciting 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 those with highly inter-dependent covariates. We further provide simulation studies as well as application to real spiking data from the mouse's lateral geniculate nucleus and the ferret's retinal ganglion cells which agree with our theoretical predictions.