Consistency of l1 Regularized Maximum Likelihood for the Poisson Distributed Data

Consider a set of Poisson distributed random variables (RV). Assume a sparse vector w which is shared among the RVs, such that the rate of the ith random variable is  wTai. The goal is to estimate w using this set of RVs. This problem is closely to related to the Compressive Sensing problem. In fact A = [a1 a2 … an]T can be considered as the sensing matrix. We will show that under the condition that A satisfies Restricted Eigenvalue condition, l1 regularized maximum likelihood estimation of w will converge to the ground truth.

  • D. Motamedvaziri, V. Saligrama, M. H. Rohban, “Sparse Signal Recovery under Poisson Statistics for Online Marketing Applications,” ICASSP 2014, (accepted).
  • D. Motamedvaziri, M. H. Rohban, V. Saligrama, “Sparse Signal Recovery under Poisson Statistics,” submitted to 51st Allerton Conference on Communication, Control, and Computing, 2013 arXiv:1307.4666 [math.ST].