A component lasso

作者：Hussami Nadine; Tibshirani Robert J

来源：Canadian Journal of Statistics, 2015, 43(4): 624-646.

DOI：10.1002/cjs.11267

• Connected components
• elastic net
• graphical lasso
• lasso
• non-negative least squares
• sparsity
• strong irrepresentable condition

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 applies the lasso to each subproblem separately, obtaining a coefficient vector for each one. Finally, 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. We prove that the component lasso is strongly sign consistent in a block-diagonal setting. 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. The modular structure of the algorithm also lends itself naturally to parallel computation.

• 出版日期2015-12