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Aaron Roth studies algorithms, machine learning and private data analysis. With Cynthia Dwork, he coauthored The Algorithmic Foundations of Differential Privacy by Cynthia Dwork and Aaron Roth, developing precise privacy guarantees and mechanisms for data analysis.^[ref]

For a count query that changes by at most one when a person's record is added or removed, the Laplace mechanism adds noise with scale $1/ϵ$ to obtain $ϵ$-differential privacy. Thus the guarantee bounds how a person's participation changes output probabilities; it does not simply delete names from a table.^[ref]

The Laplace mechanism releases a numerical query with added Laplace distribution noise scaled to the query's sensitivity. For $f(D)\in {\mathbb{R}}^k$, define its sensitivity under the chosen dataset adjacency byFor $\epsilon >0$ and positive finite sensitivity, release $f(D)+(Y_1,\dots ,Y_k)$ with independent noise coordinates of density $p(y)=(2b{)}^{-1}{e}^{-|y|/b}$, where $b={\Delta }_{1}f/\epsilon$. The ratio of output densities for adjacent inputs is bounded by $\exp (\Vert f(D)-f(D^{\prime }){\Vert }_1/b)\le e^{\epsilon }$, by the triangle inequality. Integrating over any measurable output event proves $(\epsilon ,0)$ differential privacy.^[ref]

For a count with add/remove sensitivity one and $\epsilon =0.5$, the noise scale is two and its variance is $2b^2=8$. Smaller privacy parameters increase uncertainty in this mechanism. A fixed output when sensitivity is zero needs no noise. The adjacency convention is essential: changing what one person can contribute changes the required sensitivity bound.