Clipping
As discussed earlier, unbounded queries have an infinite sensitivity value, which cannot be directly utilized to provide results with differential privacy. One approach to addressing this issue is to transform unbounded queries into bounded ones by specifying their lower and upper bounds.
In differential privacy, clipping is a technique that’s used to bind the sensitivity of a function by constraining its output within a specific range. The fundamental concept is to clip or limit the output of a function to fall into a predetermined range, such as [-c, c], where c is a positive constant. Afterward, noise is introduced to the clipped output to ensure privacy guarantees.
The clipping procedure involves two steps:
- Scaling the function’s output: The output of the function is scaled by dividing it by a scaling factor, denoted as s. This scaling ensures that the absolute value of the scaled output is less than or equal to the clipping threshold, c.
Mathematically...
