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BlockRR: A Unified Framework of RR-type Algorithms for Label Differential Privacy

Haixia Liu, Yi Ding

TL;DR

BlockRR provides a unified RR-type mechanism for label differential privacy by partitioning the label space into majority and minority blocks and applying region-specific perturbations. It unifies existing RR variants (RR, RRWithPrior, RRonBins, RPWithPrior) under a common framework and proves $\\epsilon$-Label DP, while introducing a weight-matrix–based partition to leverage label priors. Empirically, BlockRR improves the privacy-utility balance in high- and moderate-privacy regimes on imbalanced CIFAR-10 variants and avoids minority-class collapse; at low privacy budgets, it naturally reduces to standard RR, preserving utility. The work offers a practical design space for selecting RR-type strategies and highlights the potential of block-wise, prior-informed perturbations for labeled data.

Abstract

In this paper, we introduce BlockRR, a novel and unified randomized-response mechanism for label differential privacy. This framework generalizes existed RR-type mechanisms as special cases under specific parameter settings, which eliminates the need for separate, case-by-case analysis. Theoretically, we prove that BlockRR satisfies $ε$-label DP. We also design a partition method for BlockRR based on a weight matrix derived from label prior information; the parallel composition principle ensures that the composition of two such mechanisms remains $ε$-label DP. Empirically, we evaluate BlockRR on two variants of CIFAR-10 with varying degrees of class imbalance. Results show that in the high-privacy and moderate-privacy regimes ($ε\leq 3.0$), our propsed method gets a better balance between test accuaracy and the average of per-class accuracy. In the low-privacy regime ($ε\geq 4.0$), all methods reduce BlockRR to standard RR without additional performance loss.

BlockRR: A Unified Framework of RR-type Algorithms for Label Differential Privacy

TL;DR

BlockRR provides a unified RR-type mechanism for label differential privacy by partitioning the label space into majority and minority blocks and applying region-specific perturbations. It unifies existing RR variants (RR, RRWithPrior, RRonBins, RPWithPrior) under a common framework and proves -Label DP, while introducing a weight-matrix–based partition to leverage label priors. Empirically, BlockRR improves the privacy-utility balance in high- and moderate-privacy regimes on imbalanced CIFAR-10 variants and avoids minority-class collapse; at low privacy budgets, it naturally reduces to standard RR, preserving utility. The work offers a practical design space for selecting RR-type strategies and highlights the potential of block-wise, prior-informed perturbations for labeled data.

Abstract

In this paper, we introduce BlockRR, a novel and unified randomized-response mechanism for label differential privacy. This framework generalizes existed RR-type mechanisms as special cases under specific parameter settings, which eliminates the need for separate, case-by-case analysis. Theoretically, we prove that BlockRR satisfies -label DP. We also design a partition method for BlockRR based on a weight matrix derived from label prior information; the parallel composition principle ensures that the composition of two such mechanisms remains -label DP. Empirically, we evaluate BlockRR on two variants of CIFAR-10 with varying degrees of class imbalance. Results show that in the high-privacy and moderate-privacy regimes (), our propsed method gets a better balance between test accuaracy and the average of per-class accuracy. In the low-privacy regime (), all methods reduce BlockRR to standard RR without additional performance loss.
Paper Structure (24 sections, 5 theorems, 29 equations, 3 figures, 11 tables, 3 algorithms)

This paper contains 24 sections, 5 theorems, 29 equations, 3 figures, 11 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Existing RR-type Algorithms
  3. Unified Framework of RR-type algorithms under Label DP
  4. BlockRR
  5. Partition by Weight Matrix
  6. Main Idea of BlockRR
  7. Numerical Experiments
  8. Experimental Setup
  9. Datasets
  10. Experimental Details
  11. Experimental Results
  12. Ablation Study
  13. Effectness of l
  14. Sensitivity to sigma
  15. Conclusion
  16. ...and 9 more sections

Key Result

Lemma 3.1

Under the assumptions that $|B(y)|$ is constant over $y \in \mathcal{S}$ and that the partitions $\mathcal{S}_1$, $\mathcal{S}_2$, $\tilde{\mathcal{S}}_1$, $\tilde{\mathcal{S}}_2$ are fixed, $\beta$ is monotonically increasing in $l$ and $\gamma$ is monotonically decreasing in $l$. Furthermore, $\ma

Figures (3)

  • Figure 1: Quadrant view of the unified label perturbation mechanism.
  • Figure 2: Accuracy (%) versus $\sigma$ with $\epsilon\in\{0.6,0.8,1.0\}$.
  • Figure 3: Accuracy (%) versus $\sigma$ with $\epsilon\in\{2.0,3.0,4.0\}$.

Theorems & Definitions (16)

  • Definition 2.1: Differential Privacy, DP dwork2006differential
  • Definition 2.2: Label Differential Privacy, Label DP pmlr-v19-chaudhuri11a
  • Definition 2.3: Randomized Response, RR 10.1561/0400000042
  • Definition 2.4: Randomized Response with Prior, RRWithPrior ghazi2021deep
  • Definition 2.5: Randomized Response on Bins, RRonbins Ghazi2022RegressionWL
  • Definition 2.6: Regression Privacy with Prior, RPwithPrior liu2025rpwithprior
  • Lemma 3.1
  • Theorem 3.2
  • Remark 3.3
  • Theorem 3.4
  • ...and 6 more