Fig. 2.

Illustration of the computation of an optimal scaling parameter ${\widehat{s}}_i$ for Laplace noise. (A) Objective function J for fixed $\mathit{\theta }$ and different values of σ_i, showing that the kinks, i.e. the points of non-differentiability, indicated by the dashed lines are independent of σ_i. (B) Derivative of the objective function with respect to the scaling parameter which is not defined at the kinks. The light red and dark red lines indicate the computed scaling parameter and the true optimal scaling parameter, respectively