SPICE and LIKES: Two hyperparameter-free methods for sparse-parameter estimation

SPICE (SParse Iterative Covariance-based Estimation) is a recently introduced method for sparse-parameter estimation in linear models using a robust covariance fitting criterion that does not depend on any hyperparameters. In this paper we revisit the derivation of SPICE to streamline it and to provide further insights into this method. LIKES (LIKelihood-based Estimation of Sparse parameters) is a new method obtained in a hyperparameter-free manner from the maximum-likelihood principle applied to the same estimation problem as considered by SPICE. Both SPICE and LIKES are shown to provide accurate parameter estimates even from scarce data samples, with LIKES being more accurate than SPICE at the cost of an increased computational burden.