Sparse estimation of self-exciting point processes with application to LGN neural modeling

In this paper, the performance of ℓ
₁
-regularized Maximum-Likelihood estimator is investigated in sparse estimation of self-exciting processes. The underlying model includes a Generalized Linear Model (GLM) with Poisson observations and a parameter which is related to the covariates through a log-link. Kolmogorov-Smirnov and autocorrelation function tests are used as statistical goodness-of-fit measures. Results have shown a better performance of the regularized estimator both in the statistical sense and in the error norm. Application of the proposed algorithm to the LGN neuron firing data has successfully recovered the neurons' intrinsic frequencies.