Differentially Private Decentralized Dataset Synthesis Through Randomized Mixing with Correlated Noise
This work addresses privacy-utility trade-offs in federated learning for data synthesis, offering an incremental improvement over existing decentralized methods.
The paper tackles the problem of generating differentially private synthetic data in a decentralized setting, where limited local data increases noise needs and degrades utility, by integrating a correlation-assisted protocol to reduce noise through anti-correlated noise generation, achieving utility comparable to centralized methods on MNIST and FashionMNIST datasets.
In this work, we explore differentially private synthetic data generation in a decentralized-data setting by building on the recently proposed Differentially Private Class-Centric Data Aggregation (DP-CDA). DP-CDA synthesizes data in a centralized setting by mixing multiple randomly-selected samples from the same class and injecting carefully calibrated Gaussian noise, ensuring (ε, δ)-differential privacy. When deployed in a decentralized or federated setting, where each client holds only a small partition of the data, DP-CDA faces new challenges. The limited sample size per client increases the sensitivity of local computations, requiring higher noise injection to maintain the differential privacy guarantee. This, in turn, leads to a noticeable degradation in the utility compared to the centralized setting. To mitigate this issue, we integrate the Correlation-Assisted Private Estimation (CAPE) protocol into the federated DP-CDA framework and propose CAPE Assisted Federated DP-CDA algorithm. CAPE enables limited collaboration among the clients by allowing them to generate jointly distributed (anti-correlated) noise that cancels out in aggregate, while preserving privacy at the individual level. This technique significantly improves the privacy-utility trade-off in the federated setting. Extensive experiments on MNIST and FashionMNIST datasets demonstrate that the proposed CAPE Assisted Federated DP-CDA approach can achieve utility comparable to its centralized counterpart under some parameter regime, while maintaining rigorous differential privacy guarantees.