Figure 7:

Application of fwelnet to multi-task learning. n = 150, p = 50. Response 1 is a linear combination of features 1 to 10, while response 2 is a linear combination of features 1 to 5 and 11 to 15. The signal-to-noise ratios (SNR) for responses 1 and 2 are 0.5 and 1.5 respectively. The figure on the left shows the raw test mean squared error (MSE) figures with the red dotted line indicating the median null test MSE. The figure on the right shows the true positive rate (TPR) and false positive rate (FPR) of the fitted model (each point being one of 50 simulation runs). Fwelnet outperforms the individual lasso and the multi-response lasso in test MSE for both responses. Fwelnet also has better TPR and FPR than the other methods.