Efficient Agnostic Learning of Univariate Densities Under Local Differential Privacy
Read the original on arXiv Machine Learning →The paper introduces a general framework for non‑interactive locally differentially private (LDP) learning of structured univariate distributions that can be approximated by piece‑wise polynomials. It achieves the first sample‑efficient LDP learners for several distribution classes, notably mixtures of log‑concave distributions such as Gaussian mixture models (GMMs), while providing agnostic guarantees and computational efficiency. The authors also establish a new lower bound for learning GMMs under LDP, surpassing previous pure‑DP packing bounds, and develop an efficient non‑interactive LDP algorithm for synthetic data generation over large domains, which is then combined with a deterministic adaptation of a non‑private piecewise polynomial learner.
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