& $  0$ & $ 0.14$ & $ 0.22$ & $  0$ & $  0$ & $  0$\
$\ell=4$ & $  0$ & $ 0.29$ & $ 0.6$ & $ 0.02$ & $  0$ & $  0$\
$\ell=8$ & $  0$ & $ 0.3$ & $ 0.62$ & $ 0.02$ & $  0$ & $  0$\
\
$\lambda$ & $ 0.23$ & $ 0.47$ & $ 0.94$ & $ 1.9$ & $ 3.8$ & $ 7.5$\
$\ell=1$ & $  0$ & $  0$ & $  0$ & $  0$ & $  0$ & $  0$\
$\ell=2$ & $  0$ & $ 0.01$ & $ 0.01$ & $  0$ & $  0$ & $  0$\
$\ell=4$ & $  0$ & $ 0.06$ & $ 0.06$ & $  0$ & $  0$ & $  0$\
$\ell=8$ & $  0$ & $ 0.06$ & $ 0.06$ & $  0$ & $  0$ & $  0$\

Proof of Theorem \[thm:multi-stage-featsel\] {#apx:proof}
============================================

The analysis is an adaptation of [@Zhang09-multistage]. While the main proof structure is similar, there are nevertheless subtle and important differences in the details, and hence a complete proof is still necessary. The main technical differences are as follows. The proof of 