Part of Advances in Neural Information Processing Systems 37 (NeurIPS 2024) Main Conference Track
Sarvar Patel, Giuseppe Persiano, Joon Young Seo, Kevin Yeo
We study the problem of differentially private (DP) mechanisms for representingsets of size $k$ from a large universe.Our first construction creates$(\epsilon,\delta)$-DP representations with error probability of $1/(e^\epsilon + 1)$ using space at most $1.05 k \epsilon \cdot \log(e)$ bits wherethe time to construct a representation is $O(k \log(1/\delta))$ while decoding time is $O(\log(1/\delta))$.We also present a second algorithm for pure $\epsilon$-DP representations with the same error using space at most $k \epsilon \cdot \log(e)$ bits, but requiring large decoding times.Our algorithms match the lower bounds on privacy-utility trade-offs (including constants but ignoring $\delta$ factors) and we also present a new space lower boundmatching our constructions up to small constant factors.To obtain our results, we design a new approach embedding sets into random linear systemsdeviating from most prior approaches that inject noise into non-private solutions.