  Consider the problem of simultaneous estimation and support recovery of the
coefficient vector in a linear data model with additive Gaussian noise. We
study the problem of estimating the model coefficients based on a recently
proposed non-convex regularizer, namely the stochastic gates (STG) [Yamada et
al. 2020]. We suggest a new projection-based algorithm for solving the STG
regularized minimization problem, and prove convergence and support recovery
guarantees of the STG-estimator for a range of random and non-random design
matrix setups. Our new algorithm has been shown to outperform the existing STG
algorithm and other classical estimators for support recovery in various real
and synthetic data analyses.
