examples 2 (bottom left) and 4 (bottom right) do.*[]{data-label="fig:covs"}](ex3_cov.png){width="\linewidth"}

![*Heat maps of the sample covariance matrices. Examples 1 (top left) and 3 (top right) do not have a block-diagonal structure, whereas examples 2 (bottom left) and 4 (bottom right) do.*[]{data-label="fig:covs"}](ex2_cov.png){width="\linewidth"}

![*Heat maps of the sample covariance matrices. Examples 1 (top left) and 3 (top right) do not have a block-diagonal structure, whereas examples 2 (bottom left) and 4 (bottom right) do.*[]{data-label="fig:covs"}](ex4_Cov.png){width="\linewidth"}

Table \[table:allsims\] shows the results of common penalized regression methods on the above examples: the median MSE, median false positive and false negative rates. The component lasso performs well in all examples, including the ones where the data is not generated according to a covariance matrix with a block structure. The MSE achieved by the component lasso is the lowest. The use of the estimated connected components introduces a more significant improvement in example 2 when the signal variables are in the same component, and in example 4 (indicated by a \*). The model for both of these datasets has a block-diagonal covariance matrix, where certain components contain only signal variables, and the remaining components contain only noise variables. The NNLS reweighting step helps select the components containing the 