[DP-EBM] Question regarding range R and sensitivity

[Jogima-cyber]

Hello,
It appears that the range $R$ is defined to be $\max_i y_i - \min_i y_i$ in the code:

• DP noise with R: the noise is scaled by domain_size ($=R$).
• Definition of R: domain_size is set to max_target - min_target.

However with this definition of $R$ it seems to me that the sensitivity $\sum_{b \in S_{\ell}} \sum_{x_i \in \hat{H}_k (b)} y_i$ isn't $R$. Instead, it appears to be $\max\left(\max_i|y_i|, \max_i y_i - \min_i y_i\right)$. When writing the sensitivity in the case when the two samples that are different are in two different splits, one of each being $S_l$:

In this case, by taking $\max_i y_i=10000$ and $\min_i y_i=9000$ we would have $R=1000$ but the sensitivity goes up to $10000$.