Fisher Information Under Local Differential Privacy

By Leighton Pate Barnes, Wei-Ning Chen, Ayfer Özgür. 2020

60 citations recorded by the source corpus.

We develop data processing inequalities that describe how Fisher information from statistical samples can scale with the privacy parameter <inline-formula> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> under local differential privacy constraints. These bounds are valid under general conditions on the distribution of the score of the statistical model, and they elucidate under which conditions the dependence on <inline-formula> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> is linear, quadratic, or exponential. We show how these inequalities imply order-optimal lower bounds for private estimation for both the Gaussian location model and discrete distribution estimation for all levels of privacy <inline-formula> <tex-math notation="LaTeX">$\varepsilon >0$ </tex-math></inline-formula>. We further apply these inequalities to sparse Bernoulli models and demonstrate privacy mechanisms and estimators with order-matching squared <inline-formula> <tex-math notation="LaTeX">$\ell ^{2}$ </tex-math></inline-formula> error.

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Citations in the corpus

Breaking the Communication-Privacy-Accuracy Trilemma (2020, background): “, Xn and applying the lower bounds for distributional setting from [9], [51] (under an LDP constraint) and [49], [50] (under a communication constraint).”
Unified lower bounds for interactive high-dimensional estimation under information constraints (2020, background): “The average information bound in (3), in fact, allows us to recover bounds similar to the van Trees inequality-based bounds developed in [8] and [7].”
Breaking The Dimension Dependence in Sparse Distribution Estimation under Communication Constraints (2021, methodology): “In particular, without the sparse assumption, previous works (Barnes et al., 2019, 2020; Acharya et al., 2019a; Han et al., 2018b) show that the minimax `2 estimation error under b-bit and ε-local differential privacy (LDP) constraints are Θ ( d n2b ) and Θ ( d neε ) (for ε = Ω(1)).”
Estimating Sparse Discrete Distributions Under Local Privacy and Communication Constraints (2020, background): “[8] considers estimating the mean of product Bernoulli distribution when the mean vector is sparse, which is different from the k-ary setting considered in this paper.”