Re-weighting of Vector-weighted Mechanisms for Utility Maximization under Differential Privacy
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We implement a pseudo posterior synthesizer for microdata dissemination under two different vector-weighted schemes. Both schemes target high-risk records by exponentiating each of their likelihood contributions with a record-level weight, α_i ∈ [0,1] for record i ∈ (1,...,n). The first vector-weighted synthesizing mechanism computes the maximum (Lipschitz) bound, Δ_x_i, of each log-likelihood contribution over the space of parameter values, and sets the by-record weight α_i∝ 1 / Δ_x_i. The second vector-weighted synthesizer is based on constructing an identification disclosure risk probability, IR_i of record i, and setting the by-record weight α_i ∝ 1 / IR_i. We compute the overall Lipschitz bound, Δ_α,𝐱, for the database 𝐱, under each vector-weighted synthesizer such that both provide an (ϵ = 2 Δ_α,𝐱)-differential privacy (DP) formal guarantee. We propose a new vector re-weighting strategy that maximizes the data utility given any privacy budget for the vector-weighted synthesizers by adjusting the by-record weights, (α_i)_i = 1^n, such that their individual Lipschitz bounds, Δ_α,x_i, approach the bound for the entire database, Δ_α,𝐱. We illustrate our methods using simulated count data with and without over-dispersion-induced skewness and compare the results to a scalar-weighted synthesizer under the Exponential Mechanism (EM).
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