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zNm(5wTdFr}nIx8Yn`(+ct`Ghg)21d+68K?7EI(0Ae;QLADX&G#sjYG`axs)4OJ<*OoX*XD@ffiWb}(&scwr0`aCvc$vFjWR^d z;2R3e^kV0*Ui?cxKhPsmw&{y1fz`pr9obWlXdGfvq234a9tnnHmLi*Wk0;YSKK4rj zEy=c$<@4coJ-wpt*T?(<+sCf5=h9Ef literal 0 HcmV?d00001 diff --git a/EnseignementsScientifique/04_Informatique_Intellignece_articielle/4E_tests.tex b/EnseignementsScientifique/04_Informatique_Intellignece_articielle/4E_tests.tex new file mode 100644 index 0000000..072684a --- /dev/null +++ b/EnseignementsScientifique/04_Informatique_Intellignece_articielle/4E_tests.tex @@ -0,0 +1,97 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Analyse des résultats d'un test} +\date{Avril 2022} + +\pagestyle{empty} + + +\begin{document} + +\maketitle + +\begin{definition}[Paramètre d'un test - inférence Bayésienne] + On considère un test qui analyse la situation et donne deux résultats: Positif ou négatif. Une test ne peut par être sûr à 100\%, il y a donc 4 cas possibles: + + \begin{minipage}{0.45\linewidth} + \begin{tabular}{|c|c|c|c|} + \hline + & Sujet positif & Sujet négatif & Total \\ + \hline + Test positif & Vrai positif & Faux positif &\\ + \hline + Test négatif & Faux négatif & Vrai négatif & \\ + \hline + Total & & &\\ + \hline + \end{tabular} + \medskip + + Ce tableau est appelé \textbf{tableau de contingence.} + \end{minipage} + \begin{minipage}{0.5\linewidth} + \textbf{Critères de fiabilités} + \begin{itemize} + \item Sensibilité: probabilité qu'une personne infectée soit testée positive + \[ + \mbox{sensibilité} = \frac{\mbox{nombre de vrai positifs}}{\mbox{nombre de positif}} + \] + \item Spécificité: probabilité qu'une personne saine soit testée négative (vrai négatif / négatif) + \[ + \mbox{spécificité} = \frac{\mbox{nombre de vrai négatifs}}{\mbox{nombre de négatif}} + \] + \end{itemize} + \end{minipage} + +\end{definition} + +\begin{doc}{Test médical} + Un médecin cherche à déterminer si une IA est fiable. Pour cela, il a choisi 1000 dossiers de patients dont il sait que 92 d'entres eux souffrent d'un cancer. L'IA quand à elle détecte 862 cas négatif. Parmi ces cas négatifs détectés, le médecin sait que 7 d'entre eux sont malade. + + Pour déterminer si une assistance est fiable, il faut que la sensibilité soit supérieur à 90\%. +\end{doc} + +\begin{doc}{Détection d'un comportement potentiellement dangereux} + Dans le cadre du maintient de la paix, les autorités ont développer une IA qui cherche à détecter les comportements potentiellement dangereux. Suite à l'entrainement de l'IA, les données de tests donnent le tableau suivant + \begin{center} + \begin{tabular}{|p{3cm}|c|c|c|} + \hline + & Sujet dangereux & Sujet non dangereux & Total\\ + \hline + Identifier comme dangereux & 990 & 2 & \\ + \hline + Identifier comme non dangereux & 3 & 5 & \\ + \hline + Total & & & \\ + \hline + \end{tabular} + \end{center} + L'équipe en charge du projet annonce fièrement "notre IA est presque parfaite, elle ne se trompe que dans 0.5\% des cas. +\end{doc} +\vfill + +\begin{multicols}{2} + \begin{enumerate} + \item \textbf{Test médical} + \begin{enumerate} + \item Construire un tableau de contingence avec les données de l'étude. + \item Pensez vous que cette IA peut être considérer comme une assistance fiable? + \end{enumerate} + \item \textbf{Comportement dangereux} + \begin{enumerate}[leftmargin=-1pt] + \item Que pensez vous de l'affirmation de l'équipe en charge du projet? + \item Calculer la sensibilité puis la spécificité du système de détection. + \item On veut maintenant utilise cette IA dans une population de \np{1000000} individus et où l'on suppose qu'il y a 100 individus dangereux. + \begin{enumerate}[leftmargin=-1pt] + \item Reproduire le tableau de contingence en complétant la dernière ligne. + \item Compléter ensuite les autres cases vides en utilisant la sensibilité et la spécificité du test. + \item Que pensez vous de l'efficacité de ce test sur cette population? + \end{enumerate} + \item Même questions dans le cas d'une population de \np{100000} individus avec \np{500000} individus dangereux. + \end{enumerate} + \end{enumerate} +\end{multicols} + +\end{document}