Privacy-Preserving Average Consensus: Privacy Analysis and Algorithm Design
Bibliographic record
Abstract
Privacy-preserving average consensus aims to guarantee the privacy of initial states and asymptotic consensus on the exact average of the initial values. In this paper, it is achieved by adding variance-decaying and zero-sum random noises to the consensus process. However, there is lack of theoretical analysis to quantify the degree of the data privacy protection. In this paper, we introduce the maximum disclosure probability that other nodes can infer one node's initial state within a given small interval to quantify the data privacy. We utilize a novel privacy definition, named (α, β)-data-privacy, to depict the relationship between the maximum disclosure probability and the estimation accuracy. Then, we prove that the general privacy-preserving average consensus provides (α, β)-data-privacy, and obtain the closed-form expression of the relationship between α and β given the noise distribution. We reveal that the added noise with a uniform distribution is optimal in terms of achieving the highest (α, β)-data-privacy. We also prove that under what condition, the data-privacy will be compromised. Finally, an optimal privacy-preserving average consensus algorithm is proposed to achieve the highest (α, β)-data-privacy. Simulations verify the analytical results.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.019 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".