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Equation 9 · Part 3 · How Training Data and Synthetic Data Actually Work

Symbol S

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
SS

What this part means

any set of possible outcomes.

Its job in the formula

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

Where the article explains it

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.

The passage around this formula

…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 ε\varepsilon , on whether any one individual’s record was included…

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.