A MAP approach for $\ell_q$-norm regularized sparse parameter estimation using the EM algorithm
This provides an incremental improvement for researchers in statistical estimation by offering a more efficient method for sparse parameter estimation in Bayesian frameworks.
The paper tackles sparse parameter estimation by reformulating the MAP problem with an ℓq-norm penalty using the EM algorithm and variance-mean Gaussian mixtures, showing efficient optimization and handling of nonlinearities, with performance validated via simulations against a Coordinate Descent method.
In this paper, Bayesian parameter estimation through the consideration of the Maximum A Posteriori (MAP) criterion is revisited under the prism of the Expectation-Maximization (EM) algorithm. By incorporating a sparsity-promoting penalty term in the cost function of the estimation problem through the use of an appropriate prior distribution, we show how the EM algorithm can be used to efficiently solve the corresponding optimization problem. To this end, we rely on variance-mean Gaussian mixtures (VMGM) to describe the prior distribution, while we incorporate many nice features of these mixtures to our estimation problem. The corresponding MAP estimation problem is completely expressed in terms of the EM algorithm, which allows for handling nonlinearities and hidden variables that cannot be easily handled with traditional methods. For comparison purposes, we also develop a Coordinate Descent algorithm for the $\ell_q$-norm penalized problem and present the performance results via simulations.