Efficient Agnostic Learning of Univariate Densities Under Local Differential Privacy

Key points

• This gives the first sample-efficient LDP learners for several distribution classes, including mixtures of log-concave distributions, such as Gaussian mixture models (GMMs).1
• 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].1
• 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.1
• We then use it together with a deterministic adaptation of the non-private piecewise polynomial learner of Acharya et al. [ADLS17].1

Sources (1)

• [1]Efficient Agnostic Learning of Univariate Densities Under Local Differential Privacy
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 15, 12:08 AM

  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).

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