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\title[Data monetization]{Data monetization: pricing user data with the Shapley Value}
\author{Thibaut \textsc{Horel}}
\institute[Technicolor]{Work with {\greektext Στρατής \textsc{Ιωαννίδης}}}
\setbeamercovered{transparent}

\AtBeginSection[]
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\begin{frame}<beamer>
\frametitle{Outline}
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\begin{document}

\begin{frame}
\maketitle
\end{frame}

\begin{frame}{Outline}
\tableofcontents
\end{frame}

\section{Problem}
\begin{frame}{Problem Overview}

\end{frame}

\begin{frame}{Purpose}

\end{frame}

\begin{frame}{Challenges}

\end{frame}

\section{Shapley value}

\begin{frame}{Individual value}
  \begin{itemize}
  \item $S$ the set of players, a subset $S'\subset S$ is a \alert{coalition}
  \item $V: \mathcal{P}(S)\to \mathbf{R}$ the \alert{value} function:
    \begin{itemize}
    \item $V(S')$ is the value of the coalition $S'$
    \item $V(\emptyset) = 0$
    \end{itemize}
  \end{itemize}

  \alert{Question:} How to split the value of a subset across all its constituents?

  \alert{Goal:} design a function $\phi_i(S',V)$, the value of player $i$ in $S'$

  \begin{itemize}
    \visible<2->{\item $\phi_i(S',V) = V(\{i\})$?} \visible<3->{``The whole is greater than the sum of its parts''
      $$V(S')\neq \sum_{i\in S'} V(\{i\})$$}
    \visible<4->{\item $\phi_i(S',V) = V(S') - V(S'\setminus\{i\})$: the \alert{marginal contribution}?} \visible<5->{depends on the time the player joins the coalition}
  \end{itemize}
\end{frame}

\begin{frame}{Axioms}
  \begin{description}
    \item[Efficiency:] The whole value must be split
      $$V(S) = \sum_{i\in S} \phi_i(S,V)$$
    \item[Symmetry:] Equal pay for equal contribution

      \alert{if} $\forall S'\subset S\setminus\{i,j\}, V(S'\cup\{i\}) = V(S'\cup\{j\})$

      \alert{then} $\phi_i(S,V) = \phi_j(S,V)$
    \item[Fairness:] $i$'s contribution to $j$ equals $j$'s contribution to $i$
      $$\phi_i(S,V) - \phi_i(S\setminus\{j\}) = \phi_j(S,V)- \phi_j(S\setminus\{i\})$$
  \end{description}
\end{frame}

\begin{frame}{Solution: the Shapley Value}

  \begin{theorem}[Shapley, 1953]

  \end{theorem}
\end{frame}

\begin{frame}{Properties}

\end{frame}

\section{A special case}

\begin{frame}{User model}

\end{frame}

\begin{frame}{Recommender system}

\end{frame}

\begin{frame}{Value function  (1)}

\end{frame}

\begin{frame}{Properties}

\end{frame}

\begin{frame}{Value function (2)}

\end{frame}

\begin{frame}{Conclusion and future directions}

\end{frame}
\end{document}