Fig. 3.

Detection boundary $t={\rho }_{\mathrm{binary}}^{\ast }(\alpha )$ in the sparse regime when θ corresponds to logistic regression. The detectable region is $t>{\rho }_{\mathrm{binary}}^{\ast }(\alpha )$, and the undetectable region is $t<{\rho }_{\mathrm{binary}}^{\ast }(\alpha )$. The curve corresponds to $t={\rho }_{\mathrm{binary}}^{\ast }(\alpha )$.