A Component Lasso
This is an incremental improvement for researchers and practitioners in statistics and machine learning, offering enhanced performance in regression tasks.
The paper tackles the problem of sparse regression by proposing the component lasso, which splits the problem using the sample covariance matrix's connected components and recombines solutions via non-negative least squares, resulting in lower mean squared error and better support recovery compared to standard methods like lasso and elastic net.
We propose a new sparse regression method called the component lasso, based on a simple idea. The method uses the connected-components structure of the sample covariance matrix to split the problem into smaller ones. It then solves the subproblems separately, obtaining a coefficient vector for each one. Then, it uses non-negative least squares to recombine the different vectors into a single solution. This step is useful in selecting and reweighting components that are correlated with the response. Simulated and real data examples show that the component lasso can outperform standard regression methods such as the lasso and elastic net, achieving a lower mean squared error as well as better support recovery.