Does subsampling amplify privacy budget of differentially private median function

Question

I was reading that subsampling amplifies the privacy budget. I understand that it reduces the contribution of data to the aggregation function. I am wondering how sub-sampling impacts the median function. Does it amplify the privacy budget while the median is calculated using smooth sensitivity?

Answer 1

Yes. The most commonly known amplification by sampling results do not make any assumptions on the mechanism, so they will work for any DP mechanism, including median with smooth sensitivity. A nice list of such tight, generic results can be found in this paper (Theorems 8, 9, 10 and 11).