Fig. 2

Simulation Scenario 1: Density plot of estimated group importance measurement \(\left\Vert {X^{(j)}}^{\top } U\right\Vert _2/{\sqrt{p_j}}\) for each group size under 3 different noise levels. The vertical dotted red line is the average threshold. When the measurement of a group is larger than the threshold, the group is selected. The total area on the right side of the threshold under each density curve equals to the selection proportion for the corresponding group. The less the density curve spreads out, the more stable is the estimate