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\newcommand{\coursetitle}{Differential Privacy and Learning}
\newcommand{\instructor}{Gavin Brown}

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\scribeheader

Your task as a lecture scribe is to produce polished notes that will be useful for readers both in and out of the class.
You final notes should include:
\begin{itemize}
    \item A brief, informal summary of the lecture and its goals.
    \item A clean version of the information presented on the whiteboard. 
        This includes definitions, pseudocode algorithms, exercises, claims, proofs, and proofs sketches as appropriate.
		You may also need to locate citations (e.g., \cite{vadhan2017complexity,dwork2006calibrating,placeholder2026}) and include them in the bibliography.
    \item Enough additional context to make the above intelligible.
\end{itemize}
In addition to any of your personal notes from the class, you may use my handwritten notes (posted on the schedule page) and other references, such as the textbooks linked from the syllabus.
You may use AI (see note below).

The notes are not a word-for-word transcription of the class.
Thus, you do not need to include logistic questions asked by students (unless the answer clarifies things, in which case it may be good to include).

Please aim to submit your typeset notes within a week of the lecture date. 
Email your .tex file to gavin.brown@wisc.edu.
If there are any issues we will discuss and possibly iterate.
Scribing is 10\% of your grade, but it will be pass/fail; we expect that everyone will produce satisfactory notes and receive full marks.

\paragraph{Caution on AI Use}
You are welcome to use AI tools when typesetting your notes.
Of course, you are responsible for the final quality of the presentation.
In particular, in this class we may present ``standard'' concepts in non-standard ways.
In these cases, AI tools tend to steer the analysis to follow presentations in their training data.
Be on your guard about this!

\section{Example Theorem}

Here is the definition of approximate differential privacy.

\begin{definition}
An algorithm $A:\mathcal{X}^n \to \mathcal{Y}$ is \emph{$(\eps,\delta)$-differentially private} if, for all datasets $x,x'\in \mathcal{X}^n$ that differ in at most one entry and all events $E\subseteq \mathcal{Y}$, 
\[
	\Pr[A(x)\in E]\le e^\eps \Pr[A(x')\in E] + \delta.
\]
\end{definition}

Here is an example of a theorem and proof.

\begin{theorem}[Smith's Theorem]
    For every $\eps > 0$ there exists a constant $C$ such that \ldots
\end{theorem}

\begin{proof}
    Write the proof here.
\end{proof}

\section{Example Algorithm}

\cref{alg:threshold-test} gives a template for writing algorithms.

\begin{algorithm}[H]
\caption{Threshold Test}
\label{alg:threshold-test}
\begin{algorithmic}[1]
\Input Integers $x_1,\dots,x_n \in \mathbb{Z}$, threshold $T \in \mathbb{Z}$
\Returns \textsc{True} if $\sum_{i=1}^n x_i \ge T$, otherwise \textsc{False}

\State $S \gets 0$
\For{$i = 1$ to $n$}
  \State $S \gets S + x_i$
\EndFor

\If{$S \ge T$}
  \State \Return \textsc{True}
\Else
  \State \Return \textsc{False}
\EndIf

\end{algorithmic}
\end{algorithm}

\begin{thebibliography}{99}
	
\bibitem{vadhan2017complexity}
Vadhan, S.
\newblock \emph{The complexity of differential privacy}.
\newblock Tutorials on the Foundations of Cryptography, 2017.
\newblock \url{https://salil.seas.harvard.edu/sites/g/files/omnuum4266/files/salil/files/manuscript_2017.pdf}

\bibitem{dwork2006calibrating}
Dwork, C., McSherry F., Nissim, K., \& Smith, A.
\newblock \emph{Calibrating noise to sensitivity in private data analysis.}
\newblock Theory of Cryptography Conference, 2006.
\newblock \url{https://journalprivacyconfidentiality.org/index.php/jpc/article/view/405}

\bibitem{placeholder2026}
LastName, A.
\newblock \emph{Article name.}
\newblock Conference/Journal, Year.
\newblock \href{https://pages.cs.wisc.edu/~grbrown5/cs839s26/syllabus.html}{Link if possible}

\end{thebibliography}

\end{document}

