Continuous Release of Data Streams under both Centralized and Local Differential Privacy

We study the problem of publishing a stream of real-valued data satisfying differential privacy (DP). One major challenge is that the maximal possible value in the stream can be quite large, leading to enormous DP noise and bad utility. To reduce the maximal value and noise, one way is to estimate a threshold so that values above it can be truncated. The intuition is that, in many scenarios, only a few values are large; thus truncation does not change the original data much. We develop such a method that finds a suitable threshold with DP. Given the threshold, we then propose an online hierarchical method and several post-processing techniques.