Support Recovery with Stochastic Gates: Theory and Application for Linear Models
This work addresses support recovery in linear models, which is crucial for feature selection in statistics and machine learning, but it is incremental as it builds on the existing STG method.
The paper tackles the problem of estimating coefficients and recovering support in linear models with Gaussian noise by proposing a new projection-based algorithm for the stochastic gates (STG) regularizer, showing it outperforms existing methods in synthetic and real data analyses.
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.