Distributed Differentially Private Data Analytics via Secure Sketching
This work addresses privacy-utility trade-offs in distributed systems for data analysts, offering a practical intermediate model that is incremental in improving existing differential privacy frameworks.
The paper tackles the trade-off between privacy and utility in distributed data analytics by introducing the linear-transformation model, which avoids the single point of failure in central models and reduces noise compared to local models, achieving minimal error independent of client count for tasks like private low-rank approximation and ridge regression.
We introduce the linear-transformation model, a distributed model of differentially private data analysis. Clients have access to a trusted platform capable of applying a public matrix to their inputs. Such computations can be securely distributed across multiple servers using simple and efficient secure multiparty computation techniques. The linear-transformation model serves as an intermediate model between the highly expressive central model and the minimal local model. In the central model, clients have access to a trusted platform capable of applying any function to their inputs. However, this expressiveness comes at a cost, as it is often prohibitively expensive to distribute such computations, leading to the central model typically being implemented by a single trusted server. In contrast, the local model assumes no trusted platform, which forces clients to add significant noise to their data. The linear-transformation model avoids the single point of failure for privacy present in the central model, while also mitigating the high noise required in the local model. We demonstrate that linear transformations are very useful for differential privacy, allowing for the computation of linear sketches of input data. These sketches largely preserve utility for tasks such as private low-rank approximation and private ridge regression, while introducing only minimal error, critically independent of the number of clients.