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arXiv · 2610.21033

Efficient Agnostic Learning of Univariate Densities Under Local Differential Privacy

Mohammad Afzali·Hassan Ashtiani·Sivan Sabato
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Abstract

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 generation over large domains, which may be of independent interest. We then use it together with a deterministic adaptation of the non-private piecewise polynomial learner of Acharya et al. [ADLS17].

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Mohammad Afzali, Hassan Ashtiani, Sivan Sabato. 2026-10-15. Efficient Agnostic Learning of Univariate Densities Under Local Differential Privacy. https://arxiv.org/abs/2610.21033

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