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Enhancing Scalability of Metric Differential Privacy via Secret Dataset Partitioning and Benders Decomposition
May 07, 2024
Metric Differential Privacy (mDP) extends the concept of Differential Privacy (DP) to serve as a new paradigm of data perturbation. It is designed to protect secret data represented in general metric space, such as text data encoded as word embeddings or geo-location data on the road network or grid maps. To derive an optimal data perturbation mechanism under mDP, a widely used method is linear programming (LP), which, however, might suffer from a polynomial explosion of decision variables, rendering it impractical in large-scale mDP. In this paper, our objective is to develop a new computation framework to enhance the scalability of the LP-based mDP. Considering the connections established by the mDP constraints among the secret records, we partition the original secret dataset into various subsets. Building upon the partition, we reformulate the LP problem for mDP and solve it via Benders Decomposition, which is composed of two stages: (1) a master program to manage the perturbation calculation across subsets and (2) a set of subproblems, each managing the perturbation derivation within a subset. Our experimental results on multiple datasets, including geo-location data in the road network/grid maps, text data, and synthetic data, underscore our proposed mechanism's superior scalability and efficiency.
Adaptive and Cascaded Compressive Sensing
Mar 21, 2022
Scene-dependent adaptive compressive sensing (CS) has been a long pursuing goal which has huge potential in significantly improving the performance of CS. However, without accessing to the ground truth image, how to design the scene-dependent adaptive strategy is still an open-problem and the improvement in sampling efficiency is still quite limited. In this paper, a restricted isometry property (RIP) condition based error clamping is proposed, which could directly predict the reconstruction error, i.e. the difference between the currently-stage reconstructed image and the ground truth image, and adaptively allocate samples to different regions at the successive sampling stage. Furthermore, we propose a cascaded feature fusion reconstruction network that could efficiently utilize the information derived from different adaptive sampling stages. The effectiveness of the proposed adaptive and cascaded CS method is demonstrated with extensive quantitative and qualitative results, compared with the state-of-the-art CS algorithms.