The Opportunity in Difficulty: A Dynamic Privacy Budget Allocation Mechanism for Privacy-Preserving Multi-dimensional Data Collection

Data collection under local differential privacy (LDP) has been gradually on the stage. Compared with the implementation of LDP on the single attribute data collection, that on multi-dimensional data faces great challenges as follows: (1) Communication cost. Multivariate data collection needs to retain the correlations between attributes, which means that more complex privatization mechanisms will result in more communication costs. (2) Noise scale. More attributes have to share the privacy budget limited by data utility and privacy-preserving level, which means that less privacy budget can be allocated to each of them, resulting in more noise added to the data. In this work, we innovatively reverse the complex multi-dimensional attributes, i.e., the major negative factor that leads to the above difficulties, to act as a beneficial factor to improve the efficiency of privacy budget allocation, so as to realize a multi-dimensional data collection under LDP with high comprehensive performance. Specifically, we first present a Multivariate k-ary Randomized Response (kRR) mechanism, called Multi-kRR. It applies the RR directly to each attribute to reduce the communication cost. To deal with the impact of a large amount of noise, we propose a Markov-based dynamic privacy budget allocation mechanism Markov-kRR, which determines the present privacy budget (flipping probability) of an attribute related to the state of the previous attributes. Then, we fix the threshold of flipping times in Markov-kRR and propose an improved mechanism called MarkFixed-kRR, which can obtain more optimized utility by choosing the suitable threshold. Finally, extensive experiments demonstrate the efficiency and effectiveness of our proposed methods.