From this link on Differential Privacy, the L-2 sensitivity is defined as follows:
Here's my understanding of the above equation:
- Make a set of
D'data sets such that
D'is same as
Dexcept it has an absence of a one row. For each
D', calculate the given L-2 norm and return the maximum L-2 norm.
REQUIRE: D INITIALIZE empty list: norms FOR each row in D: 1. Define D` such that D` is the same as D except it doesn't have "row" in it 2. Calculate norm = ||f(D) - f(D')||_2 3. Store the norm in norms RETURN max value in norms
- Is my understanding correct?
For a machine learning task, I'm trying to perform differentially private gradient descent optimization on a data set
D by adding noise to the gradient.
In order to add Gaussian noise to the gradient, I need to calculate the L-2 sensitivity first. In my case,
f is a vector-valued function (gradient), but I think there's no issue with the definition here.