Efficient Agnostic Learning of Univariate Densities Under Local Differential Privacy
We propose a general framework for non-interactive locally differentially private (LDP) learning of structured univariate distributions that can be approximated by piece-wise polynomials. This gives the first sample-efficient LDP learners for several distribution classes, including mixtures of log-concave distributions, such as Gaussian mixture models (GMMs). These learners also provide agnostic guarantees and are computationally efficient. We also prove a lower bound for learning GMMs under LDP, improving on the standard pure-DP packing lower bounds of Bun et al. [BKSW19]. To obtain our general learning framework, we develop an efficient non-interactive LDP algorithm for synthetic data g...
| Authors | Mohammad Afzali, Hassan Ashtiani, Sivan Sabato |
|---|---|
| Primary category | stat.ML |
| Published | 15 October 2026 |
| Last updated at source | 15 October 2026 |
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