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create mode 100644 images/figures/synth/mia.pdf create mode 100644 images/figures/synth/utility.pdf diff --git a/aia.tex b/aia.tex index 76cb80e..6d4c129 100644 --- a/aia.tex +++ b/aia.tex @@ -1,3 +1,44 @@ + +\begin{frame} + \frametitle{Etude des CCA} + \begin{definition} + Un CCA est un classifieur ayant une \emph{prédiction indépendante de l'étiquette}. + C'est-à-dire que pour un classifieur $f: E\rightarrow F$. + Avec une étiquette $Y:\Omega\rightarrow F$ + et une entrée $X:\Omega\rightarrow E$. + Alors pour $\hat{Y}=f\circ X$, nous avons + \emph{$P_{(Y,\hat{Y})} = P_Y\otimes P_{\hat{Y}}$} + \end{definition} + \pause + \begin{lemma} + \label{lemme:aia-xycca} + Soit $(\Omega,\mathcal{T},P)$ un espace probabilisé. + Soient $X:(\Omega,\mathcal{T}) \rightarrow (E,\mathcal{E})$ et $Y:\Omega \rightarrow (F,\mathcal{F})$ des variables aléatoires. + Les deux propositions suivantes sont équivalentes : + \begin{enumerate} + \item $P_{(X,Y)} = P_X\otimes P_Y$. + \item Toute fonction mesurable $f:(E,\mathcal{T})\rightarrow (F,\mathcal{F})$ est un CCA pour prédire $Y$ à partir de $X$. + \end{enumerate} + \end{lemma} +\end{frame} + +\begin{frame} + \frametitle{Etude des CCA} + \begin{propriete} + \label{prop:CCA_BA} + Les CCA ayant comme image $ F$ ont une exactitude équilibrée égale à $\frac{1}{\# F}$. + \end{propriete} + \pause + \begin{theorem} + \label{th:fini-bacca} + En notant $BA(f)$ l'exactitude équilibrée de $f$. + \begin{equation*} + \forall f~BA(f)=\frac{1}{\#F} \iff + \forall f~\text{$f$ est un CCA} + \end{equation*} + \end{theorem} +\end{frame} + \begin{frame} \begin{definition}[DemParLvl] Soit $(\Omega,\mathcal{T},P$) un espace probabilisé. @@ -110,3 +151,80 @@ \label{fig:aia-data} \end{figure} \end{frame} + +\begin{frame} + \frametitle{Experimental validation on prediction: results} + \begin{figure} + \captionsetup{singlelinecheck=off} + \centering + \begin{subfigure}{0.4\textwidth} + \centering + \scriptsize + \begin{itemize} + \item \emph{Labeled Faces in the Wild (images)} + \item ML = Convolutional Neural Network + \end{itemize} + \includegraphics[width=150px]{images/figures/advdebias/lfw/lfw_advdeb_attack_hard_sex.pdf} + \end{subfigure} + \hspace{0.1\textwidth} + \begin{subfigure}{0.4\textwidth} + \centering + \scriptsize + \begin{itemize} + \item \emph{COMPAS recidivism dataset (tabular)} + \item ML = Random Forest + \end{itemize} + \includegraphics[width=150px]{images/figures/advdebias/compas/compas_advdeb_attack_hard_sex.pdf} + \end{subfigure} + \end{figure} + \vspace{10px} + + \scriptsize + \begin{tabular}{lll} + &\emph{Regularization}&\emph{Value}\\ + \emph{Baseline}&None&Attack result\\ + \emph{Theoretical}&Adversarial debiasing&$\frac{1}{2}(1+DemParLvl)$\\ + \emph{Empirical}&Adversarial debiasing&Attack result\\ + \end{tabular} +\normalsize + \hspace{10px} +Attack surface = $1_{[\tau,1]}\circ f\circ X$. +\end{frame} + +\begin{frame} + \frametitle{Experimental validation on logit: results} + \begin{figure} + \captionsetup{singlelinecheck=off} + \centering + \begin{subfigure}{0.4\textwidth} + \centering + \scriptsize + \begin{itemize} + \item \emph{Labeled Faces in the Wild (images)} + \item ML = Convolutional Neural Network + \end{itemize} + \includegraphics[width=150px]{images/figures/advdebias/lfw/lfw_advdeb_attack_soft_experimental_sex.pdf} + \end{subfigure} + \hspace{0.1\textwidth} + \begin{subfigure}{0.4\textwidth} + \centering + \scriptsize + \begin{itemize} + \item \emph{COMPAS recidivism dataset (tabular)} + \item ML = Random Forest + \end{itemize} + \includegraphics[width=150px]{images/figures/advdebias/compas/compas_advdeb_attack_soft_experimental_sex.pdf} + \end{subfigure} + \end{figure} + \vspace{10px} + + \scriptsize + \begin{tabular}{lll} + &\emph{Regularization}&\emph{Value}\\ + \emph{Baseline}&None&Attack result\\ + \emph{AdvDebias}&Adversarial debiasing&Attack result\\ + \end{tabular} +\normalsize + \hspace{10px} +Attack surface = $f\circ X$. +\end{frame} diff --git a/background.tex b/background.tex index 1cc38d6..05b96b3 100644 --- a/background.tex +++ b/background.tex @@ -11,7 +11,7 @@ \item $Y:(\Omega,\mathcal{T})\rightarrow (F,\mathcal{F})$ Les étiquettes \item $S:(\Omega,\mathcal{T})\rightarrow (G,\mathcal{G})$ L'attribut sensible \item $f:(E,\mathcal{E})\rightarrow (F,\mathcal{F})$ Le modèle d'apprentissag automatique - \item $\hat{Y}=f\circ X$ La prédiction + \item $\hat{Y}=f\circ X$ La sortie (prédiction, logit, etc.) \end{itemize} \end{frame} \begin{frame} @@ -21,7 +21,7 @@ P(f\circ X=Y) \end{equation*} \end{definition} - + \pause \begin{definition}[Exactitude équilibrée\footnote{\textit{Balanced accuracy}}] \begin{equation*} \frac{1}{\#F}\sum_{i\in F}P(f\circ X=i\mid Y=i) @@ -34,7 +34,7 @@ \label{def:background-eq-dp} $\hat{Y}$ satisfait la \emph{parité démographique} pour $S$ si et seulement si : $\forall (y,s_1,s_2)\in F\times G\times G~P(\hat{Y}=y | S=s_1) = P(\hat{Y}=y | S=s_2)$. \end{definition} - + \pause \begin{definition} \label{def:background-eq-eoo} $\hat{Y}$ satisfait l'\emph{équité des chances} pour $S$ si et seulement si : $\forall (\hat{y},y,s_1,s_2)\in E\times E\times G\times G \quad @@ -42,6 +42,17 @@ \end{definition} \end{frame} +\begin{frame} + \frametitle{Imposer l'équitée} + \emph{L'algorithme d'entraînement peut être modifié pour imposer l'équitée au modèle finale.} + \begin{itemize} + \item \textit{FairGrad: Fairness Aware Gradient Descent}, Gaurav Maheshwari and Michaël Perrot, 2022. + \item \textit{Mitigating Unwanted Biases with Adversarial Learning}, Brian Hu Zhang and Blake Lemoine and Margaret Mitchell, 2018. + \item \textit{Deep Learning with Differential Privacy}, + Martín Abadi and Andy Chu and Ian Goodfellow, 2016. + \end{itemize} +\end{frame} + \begin{frame} \frametitle{Confidentialité : Inférence de l'appartenance (MIA)} \input{tikz/attack_mia} @@ -50,11 +61,6 @@ \frametitle{Confidentialité : Inférence d'un attribut sensible (AIA)} \input{tikz/attack} \end{frame} - -\begin{frame} - \frametitle{Intersection intre confidentialité et equitée} -\end{frame} - \begin{frame} \frametitle{Pourquoi se concentrer sur ces deux enjeux ?} \begin{itemize} @@ -62,6 +68,56 @@ \pause \item Deux notions capitales pour tous les aspects de l'IA. \pause - \item La confidentialité est uniquement étudiée sous l'angle de la MIA. + \item La confidentialité est surtout étudiée sous l'angle de la MIA. \end{itemize} \end{frame} + +\begin{frame} + \frametitle{Confidentialtié différentielle} + \begin{definition}[$\varepsilon,\delta$-DP] + Soit $\mathcal{D}$ un ensemble avec la relation $\sim$. + Soit $M$ une fonction sur $\mathcal{D}$. + On dit que $M$ satisfait $\varepsilon,\delta$-DP si et seulement si + + \begin{equation} + \forall D\in\mathcal{D}~\forall D\in[D]_\sim~ + P(M(D)\in S)\leq e^{\varepsilon}P(M(D')\in S)+\delta + \end{equation} + \end{definition} +\end{frame} + +\begin{frame} + \frametitle{Intersection entre confidentialité et equitée} + \begin{itemize} + \item \emph{Il y a un compromis à faire entre équitée et MIA.} + \begin{itemize} + \item \textit{On the Privacy Risks of Algorithmic Fairness}, + Hongyan Chang and Reza Shokri, 2021. + \item \textit{Differential Privacy Has Disparate Impact on Model Accuracy}, Eugene Bagdasaryan and Cornell Tech and Omid Poursaeed and Cornell Tech and Vitaly Shmatikov, 2019. + \end{itemize} + \pause + \item \emph{L'équitée et l'AIA présentent des similariées.} + \begin{itemize} + \item \textit{Mitigating Unwanted Biases with Adversarial Learning}, Brian Hu Zhang and Blake Lemoine and Margaret Mitchell, 2018. + \end{itemize} + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Intuition} + \begin{figure} + \begin{subfigure}{0.4\textwidth} + \includegraphics[width=150px]{images/figures/before.pdf} + \caption{Avant rééquilibrage adverse\textsuperscript{1}} + \end{subfigure} + \begin{subfigure}{0.4\textwidth} + \includegraphics[width=150px]{images/figures/after.pdf} + \caption{Après rééquilibrage adverse} + \end{subfigure} + \end{figure} + \textit{Mitigating Unwanted Biases with Adversarial Learning}, Brian Hu Zhang and Blake Lemoine and Margaret Mitchell, 2018. + + \vspace{50px} + \footnotesize + \textsuperscript{1}\textit{Adversarial debiasing} +\end{frame} diff --git a/finie.tex b/finie.tex index ea42988..171d23c 100644 --- a/finie.tex +++ b/finie.tex @@ -1,43 +1,23 @@ - \begin{frame} - \frametitle{Etude des CCA} - \begin{definition} - Un CCA est un classifieur ayant une \emph{prédiction indépendante de l'étiquette}. - C'est-à-dire que pour un classifieur $f: E\rightarrow F$. - Avec une étiquette $Y:\Omega\rightarrow F$ - et une entrée $X:\Omega\rightarrow E$. - Alors pour $\hat{Y}=f\circ X$, nous avons - \emph{$P_{(Y,\hat{Y})} = P_Y\otimes P_{\hat{Y}}$} - \end{definition} - \pause - \begin{lemma} - \label{lemme:aia-xycca} - Soit $(\Omega,\mathcal{T},P)$ un espace probabilisé. - Soient $X:(\Omega,\mathcal{T}) \rightarrow (E,\mathcal{E})$ et $Y:\Omega \rightarrow (F,\mathcal{F})$ des variables aléatoires. - Les deux propositions suivantes sont équivalentes : - \begin{enumerate} - \item $P_{(X,Y)} = P_X\otimes P_Y$. - \item Toute fonction mesurable $f:(E,\mathcal{T})\rightarrow (F,\mathcal{F})$ est un CCA pour prédire $Y$ à partir de $X$. - \end{enumerate} - \end{lemma} -\end{frame} + \frametitle{Précisions sur l'AIA} + \begin{itemize} + \item + Le modèle cible est + $ + f : E\rightarrow F + $ + avec $\#F = m<\infty$. + \item + Le modèle d'attaque est + $ + a : F\rightarrow G + $ + avec $\#G=n<\infty$. + \end{itemize} -\begin{frame} - \frametitle{Etude des CCA} - \begin{propriete} - \label{prop:CCA_BA} - Les CCA ayant comme image $ F$ ont une exactitude équilibrée égale à $\frac{1}{\# F}$. - \end{propriete} - \pause - \begin{theorem} - \label{th:fini-bacca} - En notant $BA(f)$ l'exactitude équilibrée de $f$. - \begin{equation*} - \forall f~BA(f)=\frac{1}{\#F} \iff - \forall f~\text{$f$ est un CCA} - \end{equation*} - \end{theorem} \end{frame} + + \begin{frame} \frametitle{Nouvelle contribution : Classification finie} \input{tikz/ef} @@ -49,14 +29,14 @@ Plan: \begin{enumerate} \item Problème introductif : Exactitude $P(Y=f\circ X)$ - \item Exactitude équilibrée $\frac{1}{n}\sum_{i\in F}P(f\circ X=i|Y=i)$ + \item Exactitude équilibrée $\frac{1}{n}\sum_{i\in G}P(f\circ X=i|Y=i)$ \end{enumerate} \end{frame} \begin{frame} \frametitle{Classification finie} \begin{minipage}[t]{0.2\linewidth} \begin{tabular}{cc} - \textbf{X}&\textbf{Y}\\ + \textbf{Y}&\textbf{S}\\ 0&$\bigcirc$\\ 2&$\times$\\ 1&$\bigcirc$\\ @@ -74,7 +54,7 @@ \end{tabular} \end{minipage} \begin{minipage}[t]{0.75\linewidth} - On cherche une fonction $f$ de $E = \{0,1,2\}$ dans $F = \{\bigcirc,\bigtriangleup,\times\}$. + On cherche une fonction $a$ de $F = \{0,1,2\}$ dans $G = \{\bigcirc,\bigtriangleup,\times\}$. \\\vspace{0.5cm}\\ Nous n'allons pas essayer les \emph{$3^3=27$ fonctions}. \\\vspace{0.5cm}\\ @@ -90,10 +70,10 @@ \begin{theorem} L'application qui maximise l'éxactitude est \begin{equation*} - f: \left\{ + a: \left\{ \begin{matrix} - E\rightarrow F\\ - e\mapsto \text{argmax}_{i\in F} P(Y=i|X=e) + F\rightarrow G\\ + e\mapsto \text{argmax}_{i\in G} P(S=i|Y=e) \end{matrix} \right. \end{equation*} @@ -116,10 +96,10 @@ \begin{theorem} L'application qui maximise l'exactitude équilibrée est \begin{equation*} - f:\left\{ + a:\left\{ \begin{matrix} - E \rightarrow F\\ - e\mapsto \text{argmax}_{i\in F}P(X=e|Y=i) + F \rightarrow G\\ + e\mapsto \text{argmax}_{i\in G}P(Y=e|S=i) \end{matrix} \right. \end{equation*} diff --git a/images/figures/advdebias/census/census_advdeb_attack_hard_race.pdf b/images/figures/advdebias/census/census_advdeb_attack_hard_race.pdf new file mode 100644 index 0000000..a6b8ad6 Binary files /dev/null and b/images/figures/advdebias/census/census_advdeb_attack_hard_race.pdf differ diff --git a/images/figures/advdebias/census/census_advdeb_attack_hard_sex.pdf b/images/figures/advdebias/census/census_advdeb_attack_hard_sex.pdf new file mode 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\frametitle{Résultats préliminaires : impact des données synthétiques} + \begin{figure} + \begin{subfigure}{0.3\textwidth} + \includegraphics[width=\linewidth]{images/figures/synth/utility.pdf} + \caption{Utilité} + \end{subfigure} + \begin{subfigure}{0.3\textwidth} + \includegraphics[width=\linewidth]{images/figures/synth/mia.pdf} + \caption{MIA} + \end{subfigure} + \begin{subfigure}{0.3\textwidth} + \includegraphics[width=\linewidth]{images/figures/synth/aia.pdf} + \caption{AIA} + \end{subfigure} + \caption{Recensement USA (ADULT). Prédiction du salaire ($>\$50K$).} + \end{figure} +\end{frame} + +\begin{frame} + \begin{figure} + \centering + \input{tikz/synth/data_cor} + \label{fig:synth-split} + \end{figure} +\end{frame} -- cgit v1.2.3