Consistency of $\ell_1$-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 $\ell_1$-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 $n \ll p$ setting in high-dimensional statistics).


Presented at:
40th IEEE Int. Conf. Acoustics, Speech and Signal Processing, Brisbane, Australia, April 19-24, 2015
Year:
2015
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 Record created 2015-02-16, last modified 2018-09-13

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