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

Yen-Huan Li; Volkan Cevher

ICASSP 2015accepted0 citations

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

Abstract

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 ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -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).

BibTeX

@inproceedings{icassp2015_consistencyof1re,
  title = {Consistency of ℓ1-regularized maximum-likelihood for compressive Poisson regression},
  author = {Yen-Huan Li and Volkan Cevher},
  booktitle = {ICASSP 2015},
  year = {2015}
}