the MMWSE . The red dashed curve, the blue dashed-dotted curve, and the black solid curve correspond to the MMWSE of $J=1,\ 3$, and 5, respectively. The red circles, blue crosses, and black triangles represent the simulation results. We can see that our simulation results match the theoretically optimal performance.

**Remark:** The optimal weighted support set estimator  is not Lipschitz continuous. Hence, for $J=1$,  is not guaranteed to yield the MMWSE, according to Lemma \[lemma:optSMV\]. Nevertheless, numerical results for $J=1$ show that the MWSE given by  is close to the MMWSE.

For weighted support set estimation, we further study the information-theoretic optimal receiver operating characteristic (ROC) curves, which are plotted in Fig. \[fig:ROC\] for different $J$’s. The red curves and black curves are plotted for noise variances $\Delta_z=0.001$ and $0.01$, respectively. The solid curves, the dashed curves, and the dotted curves represent $J=1,\ 3$, and 5, respectively. The true positive rate (TPR) and false positive rate (FPR) in both axes are defined as TPR$=\frac{\text{\# accurately predicted positives}}{\text{\# all positives in truth}}$ and FPR$=\frac{\text{\# wrongly predicted negatives}}{\text{\# all negatives in truth}}$. We can see that having more signal vectors $J$ leads to a larger area under the ROC curve, which indicates 