Sensivity Misscalibration for the JAM algorithm

[tudorcebere]

File: mbi/mechanisms/jam.py
Lines: 231-234

Score_sensitivity_exp_mech = 2
...
selected_marg, mtype = self.exponential_mechanism(
    score_dict,
    selection_eps,
    sensitivity=score_sensitivity_exp_mech
)

Bug Description: The sensitivity of the exponential mechanism should be 4, as we are running the exp mechanism on scores computed as: model_error[m] - pub_errors[m]. Both terms depend on the private inputs and can shift by up to 2. Because these changes can occur in opposite directions, the true sensitivity is 4. The original implementation of Fuentes et al. https://github.com/Miguel-Fuentes/JAM_AiStats seems to use a sensitivity of 4, too.

Impact: The algorithm underestimates the privacy loss by underestimating sensitivity.