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Differentially Private Analysis for Binary Response Models: Optimality, Estimation, and Inference

ICML 2025 · Federated learning and privacy › Differential privacy · approach: Private data analysis frameworks

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Derives optimal randomized-response designs for LabelDP in binary response models by maximizing the trace of the Fisher information under epsilon and (epsilon, delta) constraints, and builds private confidence intervals.

Problem

Existing randomized response mechanisms for label differential privacy optimize only the response label and ignore covariates, and lack optimal estimation and inference guarantees for binary response models.

Approach

Choose RR matrix parameters (p00, p11) to maximize the trace of the Fisher information of the RR binary response model subject to epsilon- or (epsilon, delta)-LabelDP feasible regions, yielding closed-form boundary solutions and asymptotically normal MLE-based confidence intervals.

Key results

Under epsilon-LabelDP the optimal RR design has p00=p11=e^eps/(e^eps+1), and the proposed ORRbR method outperforms RRbR in MSE across simulated scenarios.
The proposed method achieves about threefold higher coverage probability for 95% confidence intervals than RRbR, close to non-private NP, per the abstract's claim.
On the plagiarism dataset, ORRbR yields lower test MSE than RRbR across privacy levels epsilon.

Measured effects reported in the paper

What was changed	Where	Measured	Effect
Use ORRbR instead of RRbR, incorporating covariate information into the randomized-response mechanism	Binary response models · Simulation studies, Scenarios I–II	MSE	Helped
Use ORRbR instead of RRbR, incorporating covariate information into the randomized-response mechanism	Binary response models · Simulation studies, Scenarios I–II	coverage probability: threefold improvement	Helped
Use ORRbR instead of RRbR	Binary response models · Plagiarism student dataset	MSE	Helped
Increase the privacy parameter ε	ORRbR · Simulation studies, Scenarios I–II	MSE	Helped
Increase the privacy parameter ε	ORRbR · Plagiarism student dataset	MSE	Helped

Surprising findings

Under tight privacy budgets the proposed method shows higher-than-nominal coverage because the privatized estimator is conservative.

Limitations

Extension to other privacy notions such as Renyi DP or Gaussian DP is unclear given the feasible region design.
Asymptotic normality results rely on large-sample assumptions; finite-sample validity shown only empirically.
Only binary responses are treated; multiclass extension is left to future work.

Experimental setup

Datasets: simulated binary response data (d=4, n=10^5) plagiarism survey data (Jann et al. 2012; 474 students)

Benchmarks: simulated logistic and probit binary response models plagiarism survey dataset (Jann et al. 2012)

Metrics: mean squared error of coefficient estimates coverage probability of 95% confidence intervals MSE of predicted probabilities on test set

Baselines: NP (non-private RR binary response) RRbR (Holohan et al. 2017 RR)

Builds on: randomized response (Warner 1965) Holohan et al. 2017 optimal RR T-optimality design criterion Fox et al. 2018 RR inference

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