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\documentclass{beamer}
\usepackage[utf8x]{inputenc}
\usepackage[greek,english]{babel}
\usepackage[LGR,T1]{fontenc}
\usepackage{lmodern}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{tikz}
\usetheme{Boadilla}
\usecolortheme{beaver}
\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[]
{
\begin{frame}<beamer>
\frametitle{Outline}
\tableofcontents[currentsection]
\end{frame}
}
\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}
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