We have values in the range $[a, b]$, and we apply a differential privacy mechanism to add noise to these values. After obtaining the noisy values, we employ the following truncation function: if a noisy value falls below $a$, it is truncated to $a$, and if the noisy value exceeds $b$, it is truncated to $b$. Does this truncation function ensure differential privacy, assuming that the mechanism itself provides differential privacy?


1 Answer 1


It depends on what you mean, namely

  1. does it maintain the level of differential privacy one gets from adding noise, or
  2. does it enhance the level of differential privacy one gets.

The answer to the first question is "trivially yes". This is because differential privacy satisfies a "data-processing inequality", in the sense that if a mechanism $M(x)$ satisfies some notion of differential privacy, then $f(M(x))$ does as well, for any function $f$.

There are certain situations where one can show that natural $f$ enhance the level of differential privacy. This is generally called "privacy amplification". I don't know if clamping does, but don't see why it would. But various other types of post-processing (for example sub-sampling) do enhance the level of differential privacy one obtains.


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