Figure 3:

“Feature of features”: grouping data. n = 100, p = 150. The features come in groups of 10, with the response being a linear combination of the features in the first group. As we go from left to right, the signal-to-noise ratio (SNR) for y increases. The figure on the left shows the test mean squared error (MSE) results with the red dotted line indicating the median null test MSE. In the figure on the right, each point depicts the true positive rate (TPR) and false positive rate (FPR) of the fitted model for one of 30 simulation runs. Fwelnet outperforms the group lasso in terms of test MSE at higher SNR levels. Fwelnet has higher TPR than the lasso, and lower FPR than the group lasso.