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Equation 9 · Part 2 · How Training Data and Synthetic Data Actually Work

Symbol D

Pr⁡[M(D)∈S]≤eε⋅Pr⁡[M(D′)∈S]+δ\Pr[\mathcal{M}(D) \in S] \le e^{\varepsilon} \cdot \Pr[\mathcal{M}(D') \in S] + \delta
DD

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D is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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D is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

…random noise before the aggregated update is applied [ 9 ] . The guarantee this produces is a specific, quantifiable one, expressed as a privacy budget: Pr⁡[M(D)∈S]≤eε⋅Pr⁡[M(D′)∈S]+δ\Pr[\mathcal{M}(D) \in S] \le e^{\varepsilon} \cdot \Pr[\mathcal{M}(D') \in S] + \delta. where M\mathcal{M} is the training mechanism, D and D' are two datasets differing by exactly one record, and S is any set of possible outcomes. In plain terms: the probability of any particular trained model (or any synthetic dataset it produces) coming out of the process is bounded so that it cannot depend too strongly, by a factor set by…

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