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Math in blockquote no worky (#84)
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For some reason that GitHub has failed to document properly, a mathematical expression in `$` is not recognized in a blockquote.  Fix that.
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martinthomson authored Feb 8, 2024
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Expand Up @@ -77,9 +77,9 @@ Thus the **dot-product** vector can be interpreted as $k$ independent dot produc

We can also ensure that the final model vector $\theta$ is *label-differentially private* by using a label-differentially-private approximation of **dot-product** in the $\nabla L$ computation.

Our privacy model assumes the private measurement system has access to training labels. Our definition of $(\epsilon, \delta)$-label differential privacy is the standard:
Our privacy model assumes the private measurement system has access to training labels.

> A randomized training algorithm $A$ taking as input a dataset is said to be $(\epsilon, \delta)$*-label differentially private* ($(\epsilon, \delta)\text{-LabelDP}$) if for any two training datasets $D$ and $D^{\prime}$ that differ in the label of a single example, and for any subset $S$ of outputs of $A$, it is the case that $Pr[A(D) \in S] \leq e^{\epsilon} \cdot Pr[A(D^{\prime}) \in S] + \delta$. If $\delta=0$, then $A$ is said to be $\epsilon$ -label differentially private ($\epsilon\text{-LabelDP}$).
Our definition of $(\epsilon, \delta)$-label differential privacy is the standard: A randomized training algorithm $A$ taking as input a dataset is said to be $(\epsilon, \delta)$*-label differentially private* ($(\epsilon, \delta)\text{-LabelDP}$) if for any two training datasets $D$ and $D^{\prime}$ that differ in the label of a single example, and for any subset $S$ of outputs of $A$, it is the case that $Pr[A(D) \in S] \leq e^{\epsilon} \cdot Pr[A(D^{\prime}) \in S] + \delta$. If $\delta=0$, then $A$ is said to be $\epsilon$ -label differentially private ($\epsilon\text{-LabelDP}$).

In the presence of a private measurement system that computes the (non-private) **dot-product** vector, label-DP can be achieved via a single-occurrence output perturbation of the form:

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