An optimization-based algorithm for model selection using an approximation of Akaike's Information Criterion

In this paper, we consider an optimization approach for model selection using Akaike's Information Criterion (AIC) by incorporating the l(0)-(pseudo)norm as a penalty function to the log-likelihood function. In order to reduce the numerical complexity of the optimization problem, we propose to approximate the l(0)-(pseudo)norm by an exponential term. We focus on problems with hidden variables- i.e. where there are random variables that we cannot measure, and the Expectation-Maximization (EM) algorithm. We illustrate the benefits of our proposal via numerical simulations.