Paper gives near-optimal private learning of discrete distributions
Original title: Efficient and Optimal Learning of Discrete Distributions with Person-Level Privacy
Polynomial-time pure and approximate DP algorithms match known sample rates up to logarithmic factors for batched user data.
A cs.CR paper studies estimating an unknown discrete distribution over k outcomes when each of n users contributes m i.i.d. samples, under person-level differential privacy and a total-variation error target. It gives polynomial-time algorithms for pure and approximate DP, with the pure-DP bound claimed to match the information-theoretic optimum up to logs. The method uses a degree-6 sum-of-squares estimator and a trace-bounded covariance certificate. The authors also prove a statistical-query lower bound against a uniformly smaller error under fixed polynomial query limits.
- Pure DP uses n on the order of k over alpha squared m, plus two further k terms.
- Approximate DP adds a log of one over delta, divided by epsilon.
- At delta of 2 to the minus Theta of k, n is tilde O of k for fixed parameters.
- The robust rate cited is O of eta times the square root of log of one over eta, over m.
From the original article
1 min read at arxiv.orgWe study learning a discrete distribution under person-level differential privacy in the batched setting. Given $n$ users, each contributing $m$ i. i.
By Gautam Kamath · arxiv.org
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