Skip to content

Commit

Permalink
Math in blockquote no worky
Browse files Browse the repository at this point in the history
For some reason that GitHub has failed to document properly, a mathematical expression in `$` is not recognized in a blockquote.  Fix that.
  • Loading branch information
martinthomson committed Oct 17, 2023
1 parent ef8fcc2 commit 6d89e3a
Showing 1 changed file with 2 additions and 2 deletions.
4 changes: 2 additions & 2 deletions logistic_regression.md
Original file line number Diff line number Diff line change
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:

Expand Down

0 comments on commit 6d89e3a

Please sign in to comment.