Efficient and Optimal Learning of Discrete Distributions with Person-Level Privacy
[Uczenie maszynowe] Autorzy: Gautam Kamath, Mahbod Majid, Ankur Moitra i 2 więcej
We study learning a discrete distribution under person-level differential privacy in the batched setting. Given $n$ users, each contributing $m$ i.i.d. samples from an unknown distribution $μ$ over $[k]$, we seek an estimate of $μ$ with total-variation error $α$. We give polynomial-time algorithms under both pure and approximate differential privacy. Under pure $(\varepsilon,0)$-DP, we achieve $n = \widetilde O(k/(α^2 m)+k/(α\sqrt{m}\varepsilon)+k/\varepsilon)$, the first polynomial-time pure-DP guarantee matching the information-theoretic optimum up to logarithmic factors. Under approximate $(\varepsilon,δ)$-DP, we achieve $n = \widetilde O(k/(α^2 m)+k/(α\sqrt{m}\varepsilon)+k+\log(1/δ)/\varepsilon)$. At $δ=2^{-Θ(k)}$, this is $\widetilde O(k)$ for fixed $α,\varepsilon,m$ and failure probability. Our algorithms use a new degree-6 sum-of-squares estimator for learning from untrusted bat…
- Kategoria arxiv
- cs.LG
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