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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]

Cynthia Dwork develops theoretical foundations for privacy-preserving data analysis. With Aaron Roth, she coauthored The Algorithmic Foundations of Differential Privacy by Cynthia Dwork and Aaron Roth. For neighboring datasets $D,D^{\prime }$ differing in one individual's contribution, pure $ϵ$-differential privacy requires, for every output event $S$,The quantifier over events protects against more than a few preselected attacks.^[ref]

For example, releasing an exact count can disclose participation when it changes from zero to one. A randomized mechanism trades some accuracy for a bound on how distinguishable those two situations become. Dwork's research account places this work within the use of theoretical computer science to formalize societal problems.^[ref]

A randomized mechanism $M$ satisfies differential privacy with parameters $(\epsilon ,\delta )$ if, for every ordered pair of adjacent datasets $D,D^{\prime }$ and measurable output event $S$,Adjacency specifies the contribution of one individual, such as adding or removing one record. The probability is over the mechanism's randomness.

For an integer count query with sensitivity one under add/remove adjacency, releasing the count plus independent Laplace distribution noise of scale $1/\epsilon$ gives $(\epsilon ,0)$ privacy. The ratio of output densities is at most $e^{\epsilon }$ by the triangle inequality. The guarantee limits distinguishability between neighboring inputs; it does not require publishing identical results or certify that every statistical estimate is accurate.^[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.

Purnamrita Sarkar works at the intersection of high-dimensional statistics, machine-learning theory, differential privacy and large-scale optimization. Her University of Texas at Austin profile describes this combination of statistical and computational research.^[ref]

Her lecture on the Efron–Stein inequality presents a general way to control the variance of a function of independent inputs: compare the function with versions in which one input is independently replaced. For a sum, the resulting bound recovers the familiar sum of variances; for a complicated estimator, it gives a route to uncertainty control without expanding every covariance term.^[ref]