Consistency of ℓ1-regularized maximum-likelihood for compressive Poisson regression

We consider Poisson regression with the canonical link function. This regression model is widely used in regression analysis involving count data; one important application in electrical engineering is transmission tomography. In this paper, we establish the variable selection consistency and estimation consistency of the ℓ₁-regularized maximum-likelihood estimator in this regression model, and characterize the asymptotic sample complexity that ensures consistency even under the compressive sensing setting (or the n ≪ p setting in high-dimensional statistics).