  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.
