How to set the privacy budget of the derived item latent matrix?

[WenyanLiu]

Question

Why the privacy budget of the derived is set as ?

Xuying Meng, Suhang Wang, Kai Shu, Jundong Li, Bo Chen, Huan Liu, Yujun Zhang: Personalized Privacy-Preserving Social Recommendation. AAAI 2018: 3796-3803

Section Modeling Sensitive and Non-sensitive Ratings, Page 4, the right column, the second paragraph from bottom

We allocate a much smaller privacy budget for sensitive ratings and a larger for non-sensitive ones where and the domain of is which is used to control the relative noise magnitude. Then sensitive ratings can receive better privacy protection with the small privacy budget . We set the privacy budget of the derived as .

Expected solution

Since sensitive and non-sensitive ratings are mutually exclusive, I am not sure if the pricacy budget of is .

Additional doubt

If the privacy budget of is , is it unfair to compare the level of privacy protection provided by PrivSR and DPMF in the experimental evaluation?