#mad

Question 1: Single choice

Wachter et al. search for a counterfactual $x'$ close to the input $x$ , measuring closeness by an L1 distance in which each feature's change is divided by that feature's median absolute deviation (MAD). What reasons do the authors give for this choice?

L1 favours changing few features; MAD puts features on comparable scales1
The L1 norm is differentiable everywhere, which makes the search easier than with L22
Dividing by the MAD forces the counterfactual to stay inside the training data3
MAD weighting makes features with a large spread expensive to change4

Timed test