An adaptive shortest-solution guided decimation approach to sparse high-dimensional linear regression
This incremental improvement addresses sparse regression for high-dimensional data, particularly in real-world applications with correlated measurements.
The authors tackled the challenge of achieving sparse regression coefficients in high-dimensional linear regression by proposing the ASSD algorithm, which outperformed LASSO, vector approximate message passing, and other greedy methods in accuracy and robustness, especially for highly correlated matrices.
High-dimensional linear regression model is the most popular statistical model for high-dimensional data, but it is quite a challenging task to achieve a sparse set of regression coefficients. In this paper, we propose a simple heuristic algorithm to construct sparse high-dimensional linear regression models, which is adapted from the shortest solution-guided decimation algorithm and is referred to as ASSD. This algorithm constructs the support of regression coefficients under the guidance of the least-squares solution of the recursively decimated linear equations, and it applies an early-stopping criterion and a second-stage thresholding procedure to refine this support. Our extensive numerical results demonstrate that ASSD outperforms LASSO, vector approximate message passing, and two other representative greedy algorithms in solution accuracy and robustness. ASSD is especially suitable for linear regression problems with highly correlated measurement matrices encountered in real-world applications.