MIST: L0 Sparse Linear Regression with Momentum
This addresses the need for efficient sparse regression methods in data analysis, but appears incremental as it builds on existing iterative shrinkage thresholding techniques.
The paper tackles the problem of estimating sparse solutions in large linear systems using an L0 penalty, proposing the MIST algorithm and proving its convergence to a local minimizer, with simulations showing superior performance on large datasets.
Significant attention has been given to minimizing a penalized least squares criterion for estimating sparse solutions to large linear systems of equations. The penalty is responsible for inducing sparsity and the natural choice is the so-called $l_0$ norm. In this paper we develop a Momentumized Iterative Shrinkage Thresholding (MIST) algorithm for minimizing the resulting non-convex criterion and prove its convergence to a local minimizer. Simulations on large data sets show superior performance of the proposed method to other methods.