Research map / Federated learning and privacy / Differential privacy
The Bernstein Mechanism: Function Release under Differential Privacy
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the iterated Bernstein approximation instead of nearest-lattice-point rounding | Private function release · Highly smooth functions | uniform approximation error: O\left(\frac{S(F)}{\varepsilon}\log(1/\beta)\right)^{\frac{h}{\ell + h}}; rounding: O(1/k^{\gamma}) | Helped |
| Use the iterated Bernstein approximation for (2h,T)-smooth functions | Bernstein mechanism · (2h,T)-smooth function release | uniform approximation error: O\left(\frac{S(F)}{\varepsilon}\log(1/\beta)\right)^{\frac{h}{\ell + h}} | Helped |
| Use the Bernstein mechanism for (γ,L)-Hölder continuous functions | Bernstein mechanism · (γ,L)-Hölder function release | uniform approximation error: O\left(\frac{S(F)}{\varepsilon}\log(1/\beta)\right)^{\frac{\gamma}{2\ell + \gamma}} | Helped |
| Use the Bernstein mechanism for linear functions | Bernstein mechanism · Linear function release | uniform approximation error: O\left(\frac{S(F)}{\varepsilon}\log(1/\beta)\right) | Helped |
| Increase the Bernstein order h | Bernstein mechanism for kernel density estimation · Kernel density estimation with Gaussian kernel | utility | Mixed |
| Release the function using the Bernstein mechanism rather than the stated baseline | Kernel density estimation · Kernel density estimation with Gaussian kernel | utility | Helped |
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