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Les résultats de l'exécution des niveaux de stacking stockent dans la mémoire des conteneurs CBR des informations qui aident à l'apprentissage de l'algorithme au fil des itérations, en plus de faciliter la génération de solutions à divers problèmes sur différentes bases de données sans avoir besoin d'une phase d'entraînement. La conception itérative en deux cycles améliore la capacité de la CBR à travailler et à s'adapter à des problèmes dynamiques en cours d'exécution, comme le montre la figure \ref{figNCBR}. @@ -44,7 +44,7 @@ L'étape de récupération utilise les algorithmes de recherche et la base de do \begin{tabular}{cccc} ID&Type&Description&Domain\\ \hline -$it$&p&Nombre d'iterations&$\mathbb{N}, it>0$\\ +$it$&p&Nombre d'itérations&$\mathbb{N}, it>0$\\ $np$&p&Nombre de processus&$\mathbb{N}, np>2$\\ $nl$&p&Nombre maximal de voisins locaux&$\mathbb{N}, nl>0$\\ $ng$&p&Nombre de voisins globaux&$\mathbb{N}, ng>2$\\ @@ -60,7 +60,7 @@ $nl_i$&v&Nombre de voisins locaux pour le modèle $i$&$\mathbb{N}, nl_i \le nl$\ $g$&v&Description de la meilleure solution globale&$\mathbb{R} ^ m$\\ $v$&v&Évaluation de la meilleure solution globale&$\mathbb{R}$\\ $d(x_1,x_2)$&f&Fonction de distance entre $x_1$ et $x_2$ &$\mathbb{R}$\\ -$MP(x_1^z,x_2,a)$&f&Fonction du modèle pour rétrouver entre $x_1$ et $x_2$&$\mathbb{R}^{a \times z}$\\ +$MP(x_1^z,x_2,a)$&f&Fonction du modèle pour retrouver entre $x_1$ et $x_2$&$\mathbb{R}^{a \times z}$\\ $MS(x_1^m)$&f&Fonction du modèle pour réutiliser avec $x_1$ &$\mathbb{R}^m$\\ $f_s(p^n,s^m)$&f&Évaluation des solutions&$\mathbb{R}$\\ \end{tabular} @@ -68,7 +68,7 @@ $f_s(p^n,s^m)$&f&Évaluation des solutions&$\mathbb{R}$\\ \label{tabVarPar} \end{table} -\subsection{Rechercher} +\subsubsection{Rechercher} La première étape de l'algorithme consiste à trouver les cas les plus similaires à un nouveau cas éventuel, pour cela un premier modèle de stacking avec différents processus est utilisé comme le montre la figure \ref{figSta1}, au niveau-0 chaque processus sélectionne et exécute un algorithme de recherche de voisins différent choisit parmi $r_a$ modèles dans le conteneur C3, avec un nombre de voisins $nl_i$ choisi aléatoirement dans l'intervalle $[0,nl]$, puis au niveau-1 les résultats sont unifiés en construisant un ensemble global de cas similaires. Cinq algorithmes pour le niveau 0 ont été mis en œuvre pour l'étape de récupération : KNN (K Nearest Neighbors), KMeans, GMM (Gaussian Mixture Model), FuzzyC et KNN Ponderation. \begin{figure} @@ -80,7 +80,7 @@ La première étape de l'algorithme consiste à trouver les cas les plus similai Formellement, le premier modèle de stacking proposé fonctionne avec deux paramètres : une base de données de $z$ cas, un cas est composé de la description du problème et de la description de la solution ${(p^n,s^m)}^{z}$ et un nouveau cas sans solution $p_w^n$, le but de tous les algorithmes de niveau 0 est de générer une liste locale de cas similaires au nouveau cas en utilisant les informations de la description du problème, c'est-à-dire que pour chaque $j$ modèle effectué, est généré l'ensemble $X_j=\{x_1,x_2,. ..,x_z \; | \; x_i=MP_i((p^n)^z, p_w^n,nl_i) \}$. Au niveau 1, un ensemble global est créé à l'aide de tous les ensembles locaux $j$ $X_g=\cup_{n=1}^{ng} min \ ; ((\cup_{j=1}^{np} X_j)-X_g)$, puis le résultat du premier modèle d'empilement est l'ensemble $X_g$ avec les $ng$ voisins les plus proches. -\subsection{Réutiliser} +\subsubsection{Réutiliser} Une fois la liste globale des cas similaires établie, les informations correspondant aux solutions de chacun de ces cas sont extraites et utilisées pour générer une nouvelle solution qui s'adapte au nouveau cas en utilisant des cas similaires et des solutions similaires, comme le montre la figure \ref{figAuto}. La génération est effectuée avec un deuxième modèle de stacking avec différents processus comme le montre la figure \ref{figSta2}, au niveau 0 chaque processus sélectionne et exécute un algorithme de génération différent à partir des modèles $r_b$ dans le conteneur C2 et au niveau 1 toutes les différentes solutions générées sont stockées dans une mémoire globale. Étant donné que la représentation des solutions est comme un tableau unidimensionnel de multiples cases, alors neuf algorithmes ont été mis en œuvre pour l'étape de réutilisation au niveau 0 : moyenne avec probabilité, moyenne sans probabilité, valeurs médianes, sélection aléatoire avec probabilité, copie et changement, vote, interpolation, ACP (analyse en composantes principales) et marche aléatoire. Tous les algorithmes proposées pour générer une nouvelle solution combinent et modifient l'ensemble de solutions construit dans l'étape de récupération. @@ -207,7 +207,7 @@ k \sim \left(\frac{1}{nl}\right) Le deuxième modèle de stacking fonctionne avec la description des solutions $s$ comme paramètre, avec l'ensemble $(s^m)^{ng}$, chaque modèle de réutilisation exécuté peut générer une solution candidate $s_{i,c}=MS_i((s^m)^{ng})$. Le niveau 1 est la construction de l'ensemble d'unification de toutes les solutions candidates $Y_g= \cup_{i=1}^{np} s_{i,c}$. Cet ensemble est évalué à l'aide d'une fonction permettant de déterminer la qualité de la solution. -\subsection{Révision} +\subsubsection{Révision} Dans cette phase, le problème de l'évaluation automatique d'une solution candidate est transformé en un problème d'optimisation, où la fonction objective est \ref{eqOpt}. Ce problème est similaire au probleme de trouver la moyenne geometrique ou problème de "Fermat-Weber", dans le cas de un espace multidimensionnel, le problème est connu comme moyenne spatiale \cite{doi:10.1137/23M1592420}. La figure \ref{fig:FW} montre un exemple de la formulation du problème en deux dimensions, où le point rouge représente une posible solution qui minimise la somme des distances avec tous les points définis dans l'espace. @@ -232,11 +232,11 @@ min \; \left( f_s(p_w^n, s_w^m) \right) = min \left( \sum_{i=1}^{ng} \lambda_i ( Le cycle d'optimisation peut exécuter les phases de récupération et de réutilisation en fonction de l'action aléatoire sélectionnée parmi $[0,at]$ à chaque itération $it$, en sauvegardant dans une mémoire globale à chaque itération la solution qui obtient la valeur minimale dans l'évaluation de la fonction objective. -\subsection{Mémorisation} +\subsubsection{Mémorisation} L'étape de rétention consiste simplement à prendre la meilleure solution proposée et à déterminer s'il s'agit d'une solution nouvelle ou existante et, si elle est nouvelle, à l'enregistrer dans la base de données. -\section{Résultats} +\subsection{Résultats} Afin de comparer les performances de prédiction et le comportement de l'algorithme proposé, dix bases de données de régression présentant des caractéristiques différentes ont été sélectionnées. Les bases de données et leurs caractéristiques sont indiquées dans le tableau \ref{tabBases}. Les valeurs des paramètres de l'algorithme sont les suivantes : $it=100$, $np=50$, $nl=10$ et $ng=10$. @@ -335,7 +335,7 @@ La dispersion globale, la médiane et les valeurs aberrantes pour quatre bases d \label{figBox} \end{figure} -\section{Discussion} +\subsection{Discussion} L'algorithme proposé révèle une performance compétitive par rapport à certains des algorithmes les plus populaires, les plus utilisés et les plus récents pour la prédiction dans les problèmes de régression. En particulier, dans ce travail, nous avons effectué les tests sur dix bases de données avec différentes caractéristiques, telles que : le nombre d'instances, le nombre de caractéristiques, le domaine des variables d'entrée, les dimensions de la variable de sortie et le domaine d'application. Cela démontre la polyvalence de l'algorithme proposé et son applicabilité à différentes configurations. Étant donné la nature exploratoire et stochastique de l'algorithme proposé, il présente une grande diversité de solutions générant plusieurs valeurs aberrantes, mais malgré cela, dans la plupart des cas, il est possible d'atteindre une solution approximative qui converge vers la solution réelle, c'est la raison pour laquelle, dans certains cas, les valeurs de la moyenne sont élevées, mais celles de la médiane restent faibles. @@ -347,13 +347,13 @@ Un aspect important de l'algorithme proposé est la fonction objective, qui peut Outre les résultats, l'algorithme proposé présente plusieurs avantages par rapport aux algorithmes avec lesquels il a été comparé, parmi lesquels : il ne nécessite pas d'entraînement, il peut intégrer des algorithmes et des règles dans chaque pile et, grâce à la conception en deux cycles, il peut travailler avec des problèmes dynamiques en cours d'exécution et la variance est faible dans les résultats produits. -\section{Conclusion} +\subsection{Conclusion} Ce chapitre propose une technique de régression générique utilisant le raisonnement fondé sur les cas et le modèle d'empilement, dont les principales caractéristiques sont qu'elle ne nécessite pas de formation et que, grâce au cycle itératif interne, elle peut s'adapter à des problèmes dynamiques en temps réel. Les résultats numériques obtenus lors des tests effectués montrent le potentiel de l'algorithme avec des données variées et des bases de données de différentes tailles ainsi que la compétitivité avec d'autres algorithmes standard et robustes couramment utilisés dans les problèmes de régression.\\\\ -\textbf{SECONDE PARTIE} +\section{SECONDE PARTIE} -\section{Modèle Proposé} +\subsection{Modèle Proposé} L'algorithme ESCBR-SMA est fondé sur le paradigme RàPC générique et incorpore divers algorithmes de recherche de voisins et de génération de solutions. Ceux-ci sont intégrés à l'aide d'une variante du modèle d'empilement en deux étapes itératives, exécutées par des agents qui exploitent indépendamment les algorithmes définis dans les conteneurs de révision et de réutilisation. Les agents possèdent une mémoire locale qui leur permet d'ajuster et de développer leur recherche de voisins, en générant des solutions à chaque itération. Chaque agent individuel a un comportement correspondant qui permet l'échange d'informations entre les autres agents. Le processus de décision et les étapes des agents au sein du système élargi sont décrits dans la figure \ref{figNCBR}. @@ -414,14 +414,14 @@ $f_s(p^n,s^m)$&f&Évaluation des solutions&$\mathbb{R}$\\ \label{tabVarPar} \end{table} -\subsection{Algorithmes} +\subsubsection{Algorithmes} Lors de la première étape de l'empilage, chaque agent peut sélectionner l'un des algorithmes mis en œuvre pour rechercher des problèmes similaires au nouveau problème posé. Les algorithmes sont les suivants : KNN (K-Nearest Neighbor), KMeans, GMM (Gaussian Mixture Model), FuzzyC et KNN pondéré. Lors de la deuxième étape de l'empilage, les agents peuvent choisir un algorithme parmi les suivants : pondération avec probabilité, pondération sans probabilité, valeurs médianes, Copier/Changer, vote, interpolation, PCA (analyse en composantes principales) et pas aléatoire. La sélection aléatoire pondérée avec l'algorithme de probabilité construit une solution en copiant aléatoirement les informations des solutions ayant une probabilité plus élevée vers le cas de problème associé le plus proche. En revanche, la sélection aléatoire pondérée sans algorithme de probabilité copie aléatoirement les informations des solutions selon la distribution uniforme. Les valeurs médianes utilisent la valeur médiane de toutes les solutions pour chaque dimension. L'algorithme fondé sur la copie/le changement copie les informations d'une solution aléatoire et en modifie une partie avec les informations d'une autre solution sélectionnée de manière aléatoire. L'algorithme fondé sur le vote copie l'information la plus fréquente entre les solutions. L'algorithme fondé sur l'interpolation utilise des informations aléatoires à partir d'une fonction d'interpolation calculée. Le générateur avec PCA transforme la description du problème en un espace de descriptions de solutions afin d'établir une relation entre le problème et sa solution. Enfin, l'algorithme de pas aléatoire sélectionne une solution et modifie les valeurs dans une seule dimension de manière aléatoire avec un petit pas dans l'espace des solutions. -\subsection{Structure des agents} +\subsubsection{Structure des agents} La structure des agents est similaire pour tous, mais chaque agent effectue un processus cognitif individuel qui lui permet d'obtenir un comportement indépendant et différent de tous les autres. La figure \ref{figAgent} montre les actions et les variables nécessaires à l'exécution de l'ensemble du processus. @@ -444,7 +444,7 @@ s_i^t=s_i^m+rn(0,d(p_w^n,p_i^n)) \label{figAgent} \end{figure} -\subsection{Apprentissage des agents} +\subsubsection{Apprentissage des agents} Tous les agents contiennent un vecteur bayésien de probabilité pour la phase de récupération (conteneur C3) et un vecteur bayésien de probabilité pour la phase de réutilisation (conteneur C2). Initialement, ces vecteurs sont configurés avec une probabilité uniforme pour tous les algorithmes de récupération et de réutilisation, il s'agit de la distribution de probabilité \textit{a priori}, mais pour chaque itération, les vecteurs sont mis à jour avec l'équation bayésienne en utilisant les meilleurs résultats du même agent comme paramètre de vraisemblance. Le choix suivant d'algorithmes pour la récupération et la réutilisation calcule la probabilité avec les vecteurs. L'agent apprend ainsi de son expérience et sélectionne les algorithmes les plus susceptibles de fournir les meilleures réponses au regard de l'objectif défini. @@ -478,11 +478,11 @@ La sélection d'un algorithme de réutilisation $a_{rs}$ se fait au moyen d'une Le processus d'apprentissage est réalisé individuellement par chaque agent, mais comporte un aspect collaboratif puisque les agents communiquent les informations qu'ils ont trouvées, les optimisations locales qu'ils ont réalisées, ainsi que les algorithmes et les paramètres. -\subsection{Échanges entre les agents} +\subsubsection{Échanges entre les agents} Les agents peuvent modifier leurs informations au cours d'une itération en choisissant au hasard un voisin dans leur liste de voisins les plus proches. Les changements permettent d'obtenir une grande probabilité de propager les paramètres des agents qui ont obtenu les meilleurs résultats et d'obtenir des effets de rétroaction. Le type d'information qu'ils peuvent modifier est choisi au hasard, il peut s'agir du nombre de voisins, de la liste des voisins les plus proches, de l'algorithme de récupération, de l'algorithme de réutilisation ou même des vecteurs bayésiens. Si un agent décide de modifier ses informations avec un voisin, les informations qu'il possédait à l'origine sont remplacées par une copie des informations obtenues auprès de l'agent sélectionné. -\section{Résultats} +\subsection{Résultats} Afin de comparer la prédiction des performances et le comportement de l'algorithme proposé, onze bases de données de régression présentant des caractéristiques différentes ont été sélectionnées. Les bases de données et leurs caractéristiques sont indiquées dans le tableau \ref{tabBases}. Les valeurs des paramètres de l'algorithme sont les suivantes $it=100$, $np=50$, $nl=10$ et $ng=10$. Les paramètres de tous les autres algorithmes sont présentés dans le tableau \ref{AlgsPar}. @@ -630,7 +630,7 @@ La dispersion globale, la médiane et les valeurs aberrantes pour toutes les bas Les résultats montrent que l'algorithme est compétitif dans la plupart des bases de données sélectionnées, obtenant les meilleurs résultats dans les bases DS2, DS4, DS5 et DS9. Globalement, d'après le classement moyen, l'algorithme est placé en troisième position, à proximité d'autres algorithmes d'ensemble. Par rapport à l'ESCBR, une amélioration des résultats et une réduction de la variance ont été obtenues, ce qui montre que les systèmes multi-agents et le raisonnement stochastique bayésien contribuent à l'apprentissage et à la convergence de l'algorithme vers des solutions plus proches de la solution réelle. -\section{Conclusion} +\subsection{Conclusion} L'ECBR proposé avec SMA tente d'utiliser les avantages des systèmes multi-agents pour améliorer la qualité des solutions proposées ainsi que pour améliorer le processus d'apprentissage global afin d'augmenter la performance de l'algorithme à chaque nouvelle exécution même sur des données différentes, il utilise également le raisonnement bayésien qui permet d'obtenir de bonnes approximations et un apprentissage optimal avec peu de données. Ce travail a démontré la capacité du modèle à trouver des solutions proches de l'optimum global pour la majorité des ensembles de données analysés, même avec des ensembles de données divers, déséquilibrés et de tailles différentes. Les résultats montrent en effet une amélioration de l'ECBR de base, qui peut être due à la combinaison du potentiel de l'ECBR et des caractéristiques des systèmes multi-agents tels que les effets de rétroaction, les effets émergents et le comportement de raisonnement bayésien cognitif mis en œuvre. diff --git a/chapters/Publications.aux b/chapters/Publications.aux index 34da215..0258991 100644 --- a/chapters/Publications.aux +++ b/chapters/Publications.aux @@ -40,7 +40,7 @@ \setcounter{section@level}{1} \setcounter{Item}{0} \setcounter{Hfootnote}{0} -\setcounter{bookmark@seq@number}{86} +\setcounter{bookmark@seq@number}{91} \setcounter{DefaultLines}{2} \setcounter{DefaultDepth}{0} \setcounter{L@lines}{3} diff --git a/chapters/TS.aux b/chapters/TS.aux index 66e776e..3f344e5 100644 --- a/chapters/TS.aux +++ b/chapters/TS.aux @@ -8,7 +8,8 @@ \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {7.1}Introduction}{73}{section.7.1}\protected@file@percent } \citation{Liu2023} -\@writefile{toc}{\contentsline {section}{\numberline {7.2}Modèle Proposé}{74}{section.7.2}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\numberline {7.2}PREMIÈRE PARTIE}{74}{section.7.2}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.1}Modèle Proposé}{74}{subsection.7.2.1}\protected@file@percent } \newlabel{eqBeta}{{7.1}{75}{Modèle Proposé}{equation.7.2.1}{}} \@writefile{lot}{\contentsline {table}{\numberline {7.1}{\ignorespaces Variables et paramètres du modèle proposé\relax }}{75}{table.caption.44}\protected@file@percent } \newlabel{tabPar}{{7.1}{75}{Variables et paramètres du modèle proposé\relax }{table.caption.44}{}} @@ -21,7 +22,7 @@ \newlabel{eqsGT}{{7.7}{76}{Modèle Proposé}{equation.7.2.7}{}} \@writefile{loa}{\contentsline {algorithm}{\numberline {1}{\ignorespaces Stochastic Recommendation Model\relax }}{76}{algorithm.1}\protected@file@percent } \newlabel{alg2}{{1}{76}{Stochastic Recommendation Model\relax }{algorithm.1}{}} -\@writefile{toc}{\contentsline {section}{\numberline {7.3}Résultats}{76}{section.7.3}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {7.2.2}Résultats}{76}{subsection.7.2.2}\protected@file@percent } \@writefile{lof}{\contentsline {figure}{\numberline {7.1}{\ignorespaces Boîte à moustaches pour la base de données générée\relax }}{77}{figure.caption.45}\protected@file@percent } \newlabel{figData}{{7.1}{77}{Boîte à moustaches pour la base de données générée\relax }{figure.caption.45}{}} \@writefile{lot}{\contentsline {table}{\numberline {7.2}{\ignorespaces Description des variables utilisées dans la base de données evaluée\relax }}{77}{table.caption.46}\protected@file@percent } @@ -32,114 +33,116 @@ \newlabel{figCmp2}{{7.2}{78}{Résultats pour le premier test\relax }{figure.caption.48}{}} \@writefile{lof}{\contentsline {figure}{\numberline {7.3}{\ignorespaces Résultats pour le deuxième Test\relax }}{79}{figure.caption.49}\protected@file@percent } \newlabel{figCmp3}{{7.3}{79}{Résultats pour le deuxième Test\relax }{figure.caption.49}{}} -\newlabel{eqMetric1}{{7.8}{79}{Résultats}{equation.7.3.8}{}} -\newlabel{eqMetric2}{{7.9}{79}{Résultats}{equation.7.3.9}{}} +\newlabel{eqMetric1}{{7.8}{79}{Résultats}{equation.7.2.8}{}} +\newlabel{eqMetric2}{{7.9}{79}{Résultats}{equation.7.2.9}{}} \@writefile{lof}{\contentsline {figure}{\numberline {7.4}{\ignorespaces Résultats pour le troisième Test\relax }}{80}{figure.caption.50}\protected@file@percent } \newlabel{figCmp4}{{7.4}{80}{Résultats pour le troisième Test\relax }{figure.caption.50}{}} -\newlabel{eqXc}{{7.10}{80}{Résultats}{equation.7.3.10}{}} -\newlabel{eqYc}{{7.11}{80}{Résultats}{equation.7.3.11}{}} +\newlabel{eqXc}{{7.10}{80}{Résultats}{equation.7.2.10}{}} +\newlabel{eqYc}{{7.11}{80}{Résultats}{equation.7.2.11}{}} \@writefile{lot}{\contentsline {table}{\numberline {7.4}{\ignorespaces Résultats de la métrique $rp_c(x)$ (CBR - 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Bottom: dynamic learning process with Hawkes process)\relax }}{102}{figure.caption.69}\protected@file@percent } @@ -155,8 +158,8 @@ \setcounter{mpfootnote}{0} \setcounter{part}{3} \setcounter{chapter}{7} -\setcounter{section}{11} -\setcounter{subsection}{0} +\setcounter{section}{4} +\setcounter{subsection}{3} \setcounter{subsubsection}{0} \setcounter{paragraph}{0} \setcounter{subparagraph}{0} @@ -171,15 +174,15 @@ \setcounter{vrcnt}{0} \setcounter{upm@subfigure@count}{0} \setcounter{upm@fmt@mtabular@columnnumber}{0} -\setcounter{upm@format@section@sectionlevel}{1} +\setcounter{upm@format@section@sectionlevel}{2} \setcounter{upm@fmt@savedcounter}{0} \setcounter{@@upm@fmt@inlineenumeration}{0} \setcounter{@upm@fmt@enumdescription@cnt@}{0} \setcounter{upmdefinition}{0} -\setcounter{section@level}{1} +\setcounter{section@level}{2} \setcounter{Item}{0} \setcounter{Hfootnote}{0} -\setcounter{bookmark@seq@number}{83} +\setcounter{bookmark@seq@number}{88} \setcounter{DefaultLines}{2} \setcounter{DefaultDepth}{0} \setcounter{L@lines}{3} diff --git a/chapters/TS.tex b/chapters/TS.tex index 90c3d0b..a9f8a65 100644 --- a/chapters/TS.tex +++ b/chapters/TS.tex @@ -27,9 +27,9 @@ Dans la troisième partie seront détaillées les contributions réalisées avec \item Vérification de la progression, de la stabilité, la précision et évolution de l'algorithme de recommandation stochastique proposé à l'aide de bases de données simulées et hétérogènes d'étudiants réels.\\\\ \end{itemize} -\textbf{PREMIÈRE PARTIE} +\section{PREMIÈRE PARTIE} -\section{Modèle Proposé} +\subsection{Modèle Proposé} Le modèle proposé, en tant que système de recommandation, prend en compte les notes antérieures des apprenants pour estimer leurs connaissances et leur maîtrise des différentes compétences, sous-compétences et niveaux de complexité au sein du système AI-VT, puis adapte les sessions pour maximiser l'acquisition des connaissances et la maîtrise des différents domaines contenus dans la même compétence définie. Le modèle est conçu comme une modification de l'algorithme d'échantillonnage de Thompson avec l'intégration de l'échantillonnage stratifié pour obtenir l'adaptation. @@ -141,7 +141,7 @@ Le détail des pas d'exécution du modèle proposé sont dans l'algorithme \ref{ \label{alg2} \end{algorithm} -\section{Résultats} +\subsection{Résultats} Le comportement du modèle a été testé avec un jeu de données généré, ce jeu de données contient les notes et les temps de réponse de 1000 apprenants pour 5 niveaux de complexité différents, la description des données est indiquée dans le Tableau \ref{tabDataSet}. Les notes des apprenants sont générées avec la distribution logit-normale de probabilité, car c'est expérimentalement le meilleur modèle de représentation \cite{Arthurs}. @@ -351,7 +351,7 @@ SM&\textbf{0.8124}&\textbf{0.8856}&\textbf{0.9244}\\ \label{tabCS} \end{table} -\section{Discussion et Conclusions} +\subsection{Discussion et Conclusions} Avec la génération d'exercices CBR, le système propose les mêmes exercices à tous les apprenants, et l'évolution des niveaux de complexité est très lente, presque un changement toutes les 3 ou 4 sessions, ceci parce que le système ne prend pas en compte les notes obtenues pendant la session. Les systèmes de recommandation sont plus dynamiques et les évolutions sont plus rapides mais en considérant les notes des apprenants, le modèle déterministe suggère des changements de niveaux à un grand nombre d'apprenants soudainement parce qu'ils sont regroupés à l'intérieur d'un intervalle de taux de maîtrise, alors que le modèle stochastique est plus axé sur la personnalisation individuelle et les changements de niveau de complexité sont produits pour un petit nombre d'apprenants. Les deux modèles proposés ont la capacité de détecter les faiblesses des apprenants et d'adapter la session à leurs besoins particuliers. La base de données générée a permis de simuler diverses situations avec les notes de 1000 apprenants, permettant ainsi d'évaluer le comportement des systèmes de recommandation avec différentes configurations. @@ -362,9 +362,9 @@ Selon la métrique de la similarité cosinus, le modèle de recommandation propo Les modules de recommandation sont une pièce essentielle pour les systèmes ITS car ils aident à guider le processus d'apprentissage individuel, permettent d'identifier les faiblesses et de réorienter le processus complet afin d'améliorer les connaissances et les compétences. Les versions du modèle proposé peuvent détecter en temps réel les faiblesses de l'apprenant et tentent de réorienter la session vers le meilleur niveau de complexité possible afin d'aider l'apprenant à acquérir et à maîtriser les connaissances avant de passer aux niveaux de complexité supérieurs, car généralement les connaissances des niveaux de complexité inférieurs sont nécessaires pour compléter les niveaux supérieurs. Même si l'ensemble de données généré est une simulation des temps de réponse et des notes des apprenants, les tests qui l'utilisent permettent de voir la flexibilité et la robustesse du modèle de recommandation proposé, car les données relatives aux apprenants présentent une grande diversité et obligent le système à s'adapter à différents types de configurations. Par conséquent, il est possible de conclure que le modèle de recommandation proposé a la capacité de fonctionner dans différentes situations et dans chaque cas de proposer des chemins alternatifs pour améliorer le processus d'apprentissage global, même si l'objectif d'apprentissage est différent pour chaque apprenant, comme le démontrent les résultats obtenus dans l'évaluation des deux métriques proposées. Le modèle proposé permet également la diversité et la personnalisation du système, puisque selon les résultats de la comparaison avec la similarité cosinus entre toutes les recommandations générées pour chaque apprenant, il y a une augmentation par rapport au système original.\\\\ -\textbf{DEUXIÈME PARTIE} +\section{DEUXIÈME PARTIE} -\section{Concepts Associés} +\subsection{Concepts Associés} Cette section présente les concepts, les définitions et les algorithmes nécessaires à la compréhension du modèle proposé, ainsi que les modèles et les mesures fondamentaux. Le premier paradigme fondamental utilisé dans ce travail est le raisonnement à partir de cas (CBR), qui permet d'exploiter les connaissances historiquement acquises et l'expérience accumulée en ce qui concerne un problème spécifique. Ce paradigme est utilisé pour générer des solutions émergentes pour un nouveau problème en utilisant une base de données de connaissances. L'idée principale est de rechercher des situations antérieures similaires et d'utiliser l'expérience acquise pour résoudre de nouveaux problèmes. La CBR est particulièrement utile lorsque les causes sous-jacentes d'un problème ne sont pas bien comprises. Le raisonnement à base de cas définit un cycle de quatre étapes pour améliorer la solution d'inférence \cite{jmse11050890}. @@ -489,7 +489,7 @@ Les distributions de probabilité à comparer doivent être continues et défini La prédiction utilisée dans le modèle proposé est fondée sur les travaux de Soto \textit{et al.} \cite{10.1007/978-3-031-63646-2_11}, il s'agit d'un modèle d'empilage de raisonnement à partir de cas qui met en œuvre deux niveaux d'intégration, le modèle utilise globalement la stratégie d'empilage pour exécuter plusieurs algorithmes afin de rechercher des informations dans un ensemble de données et de générer des solutions à différents problèmes génériques, en outre il y a une étape d'évaluation qui permet de sélectionner la solution la plus optimale pour un problème donné en fonction d'une métrique adaptative définie pour les problèmes de régression. Il a été décidé de mettre en œuvre le modèle fondé sur l'empilement car il s'agit d'une méthode d'ensemble qui permet d'éviter le paradoxe de Stein puisqu'elle combine les points de vue de différents estimateurs à des étapes de récupération et de réutilisation par raisonnement à partir de cas. -\section{Modèle Proposé} +\subsection{Modèle Proposé} Le modèle proposé est une intégration du modèle d'adaptation stochastique (fondé sur l'échantillonnage de Thompson) avec le raisonnement à base de cas d'ensemble (ESCBR-SMA). Dans ce cas, le modèle de recommandation produit une adaptation en fonction des notes de l'apprenant et l'ESCBR-SMA effectue une prédiction pour valider l'adaptation générée. @@ -546,7 +546,7 @@ L'intégration se fait en trois étapes. Tout d'abord, il est nécessaire d'avoi Avec les valeurs finales calculées pour chaque niveau de complexité, le niveau de complexité qui a la valeur la plus élevée est proposé comme recommandation finale (équation \ref{eqMixModels}). Le niveau de complexité qui a la valeur la plus élevée est proposé comme recommandation finale (équation \ref{eqMixModels}). -\section{Résultats et Discussion} +\subsection{Résultats et Discussion} Cette section présente la description de la base de données et les paramètres utilisés pour mesurer la précision, la performance et la progression des connaissances, les résultats individuels du modèle de recommandation, le modèle de prédiction ainsi que leur intégration finale pour améliorer la personnalisation du système d'IA-VT. Cette section présente les résultats individuels du modèle de recommandation, le modèle de prédiction ainsi que leur intégration finale pour améliorer la personnalisation du système d'IA-VT. @@ -556,7 +556,7 @@ Le principal inconvénient de ce système de validation « en situation réelle Quatre tests différents ont été effectués pour démontrer les avantages de l'intégration de la TS et de la CBR dans les EIAH. Le premier est l'utilisation de CBR pour la régression avec une base de données d'apprenants afin de démontrer la capacité du modèle à prédire les notes à différents niveaux de complexité, le deuxième est l'évaluation de la progression des connaissances avec TS afin de déterminer l'efficacité du modèle dans la recommandation personnalisée pour chaque apprenant, La troisième est la comparaison entre les modèles de recommandation BKT et TS afin d'établir la performance du modèle TS en utilisant BKT comme modèle de base et enfin, la comparaison entre TS seul et TS avec ESCBR-SMA pour démontrer que l'intégration entre les deux modèles améliore l'ensemble du système de recommandation dans AI-VT. -\subsection{Régression dans la base de données des apprenants avec ESCBR-SMA} +\subsubsection{Régression dans la base de données des apprenants avec ESCBR-SMA} Le SMA utilise le raisonnement bayésien, ce qui permet aux agents d'apprendre des données et des interactions au cours de l'exécution et de l'exploration. @@ -626,7 +626,7 @@ E1 (RMSE)&0.625&0.565&0.741&0.56&0.606&0.626&0.626&0.681&0.541&\textbf{0.54}\\ \label{tab:results} \end{table} -\subsection{Progression des connaissances} +\subsubsection{Progression des connaissances} Le modèle de recommandation TS est fondé sur le paradigme bayésien, ce qui est très utile lorsque les données sont limitées et l'incertitude forte. Afin de quantifier la connaissance et de voir sa progression dans le temps avec TS, la divergence de Jensen-Shannon avec la famille de distribution Beta en $t$ et $t-1$ fois a été utilisée comme second test. L'équation \ref{eqprog1} décrit formellement le calcul à effectuer avec les distributions de probabilité en un temps $t$ pour un niveau de complexité $c$, en utilisant la définition $m$ (équation \ref{eqprog2}). @@ -667,7 +667,7 @@ La progression totale des connaissances en $t$ est la somme des différences ent \label{eqTEK} \end{equation} -\begin{figure} +\begin{figure}[!ht] \centering \includegraphics[width=\textwidth]{Figures/kEvol_TS.jpg} \caption{Progression des connaissances avec l'échantillonnage de Thompson selon la divergence de Jensen-Shannon} @@ -676,7 +676,7 @@ La progression totale des connaissances en $t$ est la somme des différences ent La figure \ref{fig:evolution} montre la progression cumulative des connaissances sur les quinze questions d'une seule session de formation. Entre la première et la dernière question de la même session, tous les apprenants ont statistiquement augmenté leur niveau de connaissance puisque la moyenne a augmenté, la variabilité augmente à partir de la première question jusqu'à la question neuf, où le système a acquis plus d'informations sur les apprenants, à partir de là la variabilité diminue et la moyenne augmente. La figure {fig:evolution} montre la progression cumulative des connaissances sur les quinze questions d'une même session de formation. -\subsection{Comparaison entre TS et BKT} +\subsubsection{Comparaison entre TS et BKT} L'évolution du système de recommandation TS est testée en comparaison avec BKT, la figure \ref{fig:EvGrades} montre l'évolution des notes des apprenants en fonction du nombre de questions auxquelles ils répondent dans la même session. Dans ce cas, le modèle TS génère moins de variabilité que BKT, mais si est faite la comparaison des moyennes générées par chaque question, l'évolution est très similaire. La figure \ref{fig:EvGrades} montre l'évolution des notes des apprenants en fonction du nombre de questions auxquelles ils répondent au cours de la même session. @@ -687,7 +687,7 @@ L'évolution du système de recommandation TS est testée en comparaison avec BK \label{fig:EvGrades} \end{figure} -Mais, si les résultats obtenus sont comparés par rapport à l'évolution du niveau de complexité recommandé (figure \ref{fig:EvCL}), le modèle TS fait évoluer le niveau de complexité des apprénants, alors que le modèle BKT a tendance à laisser les apprénants au même niveau de complexité, c'est-à-dire qu'avec le modèle BKT, il est difficile d'apprendre de nouveaux sujets ou des concepts plus complexes au sein du même domaine. En examinant les résultats des deux figures (figures \ref{fig:EvGrades} et \ref{fig:EvCL}) et en établissant des comparaisons, le modèle TS permet de progresser en moyenne dans la valeur des notes et facilite l'évolution des niveaux de complexité.\N- Le modèle TS permet de progresser en moyenne dans la valeur des notes et facilite l'évolution des niveaux de complexité. Le modèle TS permet de progresser en moyenne dans la valeur des notes et facilite l'évolution des niveaux de complexité. +Mais, si les résultats obtenus sont comparés par rapport à l'évolution du niveau de complexité recommandé (figure \ref{fig:EvCL}), le modèle TS fait évoluer le niveau de complexité des apprenants, alors que le modèle BKT a tendance à laisser les apprenants au même niveau de complexité, c'est-à-dire qu'avec le modèle BKT, il est difficile d'apprendre de nouveaux sujets ou des concepts plus complexes au sein du même domaine. En examinant les résultats des deux figures (figures \ref{fig:EvGrades} et \ref{fig:EvCL}) et en établissant des comparaisons, le modèle TS permet de progresser en moyenne dans la valeur des notes et facilite l'évolution des niveaux de complexité.\N- Le modèle TS permet de progresser en moyenne dans la valeur des notes et facilite l'évolution des niveaux de complexité. Le modèle TS permet de progresser en moyenne dans la valeur des notes et facilite l'évolution des niveaux de complexité. \begin{figure} \centering @@ -696,13 +696,13 @@ Mais, si les résultats obtenus sont comparés par rapport à l'évolution du ni \label{fig:EvCL} \end{figure} -\subsection{Système de recommandation avec ESCBR-SMA} +\subsubsection{Système de recommandation avec ESCBR-SMA} Le troisième test est l'intégration entre deux modèles. Cette combinaison est faite pour éviter le paradoxe de Stein, en essayant de combiner des observations qui ne sont pas directement liées l'une à l'autre, c'est-à-dire en utilisant l'information individuelle (Thomson sampling recommender) et le filtre collaboratif (Case-base reasoning prediction) pour améliorer la personnalisation. Le test est une comparaison entre le système de recommandation TS et le système de recommandation TS avec la prédiction ESCBR-SMA afin de déterminer si l'intégration des deux modèles permet d'améliorer l'évolution du processus d'apprentissage proposé par le système AI-VT. La comparaison est effectuée après la question 6 pour tous les apprenants, car il est nécessaire de disposer d'informations préalables pour utiliser l'algorithme ESCBR-SMA et prédire les notes dans tous les niveaux de complexité pour la question suivante. -\subsection{Progression des connaissances TS vs TS et ESCBR-SMA} +\subsubsection{Progression des connaissances TS vs TS et ESCBR-SMA} Pour établir la différence entre le modèle de recommandation TS et le même modèle associé à la prédiction fondée sur le raisonnement à partir de cas ESCBR-SMA, le quatrième test est défini en utilisant la métrique de Jensen-Shannon, mais dans ce cas la comparaison est faite entre les différents modèles (TS, TS-ESCBR) sur le même niveau de complexité dans le même temps $t$. La définition formelle de la métrique est exprimée par les équations \ref{eqjs4} et \ref{eqjs5}. La définition formelle de la métrique est exprimée par les équations \ref{eqjs4} et \ref{eqjs5}. @@ -733,16 +733,16 @@ La comparaison entre l'évolution des connaissances présente une bifurcation ap \label{fig_cmp2} \end{figure} -\section{Conclusion} +\subsection{Conclusion} Ce chapitre présente un modèle intégré entre deux modèles développés précédemment, un système de recommandation fondé sur l'algorithme d'échantillonnage de Thompson et un modèle de régression d'ensemble fondé sur le raisonnement par cas. Le modèle intégré est appliqué à un ITS appelé AI-VT, les résultats montrent en effet que l'intégration permet d'améliorer la performance des deux modèles utilisés séparément, en outre il montre de meilleurs résultats dans la révision/adaptation des étapes de solutions pour chaque apprenant, en fonction des métriques utilisées et des tests définis, donnant une meilleure personnalisation du système et facilitant l'acquisition de connaissances. %Le modèle intégré est appliqué à un ITS appelé AI-VT.\\ Les avantages du modèle proposé sont les suivants : i) il permet de générer des recommandations personnalisées pour chaque apprenant avec relativement peu de données historiques, ii) étant donné que de multiples points de vue (différents algorithmes) sur le même problème et avec la même base de données sont intégrés, le risque de tomber dans des paradoxes statistiques (Stein, Simpson) est réduit, iii) les deux modèles se complètent mutuellement en améliorant les résultats finaux d'une manière généralisée. Le modèle proposé a été conçu pour être utilisé dans le cadre d'un projet de recherche et de développement en cours.\\\\ -\textbf{TROISIÈME PARTIE} +\section{TROISIÈME PARTIE} -\section{Modèle Proposé} +\subsection{Modèle Proposé} L'algorithme proposé est une intégration de la recommandation stochastique (fondée sur l'échantillonnage de Thompson), du raisonnement à partir de cas (ESCBR-SMA) et du processus de Hawkes. Dans ce cas, l'algorithme de recommandation produit une adaptation en fonction des notes de l'apprenant et l'ESCBR-SMA effectue une prédiction pour valider l'adaptation générée, le processus de Hawkes simule la courbe d'oubli dans le processus d'apprentissage. L'idée de l'unification est d'obtenir des informations d'un point de vue local où une recommandation est obtenue en se basant uniquement sur les informations des apprenants individuels (modèle fondé sur l'échantillonnage de Thompson), la prédiction globale où les informations sont obtenues à partir de tous les apprenants qui ont des résultats similaires (filtre collaboratif avec CBR) et le processus d'apprentissage dynamique avec le processus de Hawkes. L'architecture de l'algorithme est présentée dans la figure \ref{fig:Amodel}, où TS et CBR sont exécutés en parallèle et indépendamment avec les informations extraites de la même base de données, une fois que les résultats de chaque algorithme sont obtenus, les résultats sont unifiés par une fonction de pondération et une distribution de probabilité mises à jour dynamiquement en fonction des événements passés et du niveau de complexité sélectionné, la recommandation finale est celle qui maximise l'expression \ref{eqMixModels}. La consolidation des deux résultats globaux permet d'atténuer l'effet du paradoxe de Simpson \cite{10.1145/3578337.3605122}. @@ -849,23 +849,23 @@ And for each complexity level $c$, the equation \ref{eqBetaH} describe the distr \label{eqBetaH} \end{equation} -\section{Résultats et Discussion} +\subsection{Résultats et Discussion} -\subsection{Système de recommandation avec une base de données d'étudiants réels (TS avec Hawkes)} +\subsubsection{Système de recommandation avec une base de données d'étudiants réels (TS avec Hawkes)} Le système de recommandation TS a été testé avec un ensemble de données adapté extrait des données réelles des interactions des étudiants avec un environnement d'apprentissage virtuel pour différents cours \cite{Kuzilek2017}, le total des apprenants est 23366, dans cette base de données il y a les notes de l'apprenant dans différents cours et de multiples types d'évaluations. Il s'agit du troisième test, pour lequel le format de la base de données est adapté à la structure AI-VT (notes, temps de réponse et niveau de complexité), les niveaux de complexité sont divisés en cinq étapes et calculés avec le pourcentage de poids défini dans l'ensemble de données. La figure \ref{fig:stabilityBP} a été générée après 100 exécutions de l'algorithme et montre que même la stochasticité, l'algorithme est stable parce que la variance globale dans tous les niveaux de complexité est faible en fonction du nombre total d'apprenants et du nombre total de recommandations. \begin{figure}[!ht] \centering - \includegraphics[width=0.6\textwidth]{./Figures/stabilityBoxplot1.png}\hfill - \includegraphics[width=0.6\textwidth]{Figures/stabilityBoxplot2.png} + \includegraphics[width=\textwidth]{./Figures/stabilityBoxplot1.png}\hfill + \includegraphics[width=\textwidth]{./Figures/stabilityBoxplot2.png} \caption{Number of recommendations by complexity level (left static learning process, right dynamic learning process with Hawkes process)} \label{fig:stabilityBP} \end{figure} L'algorithme recommande plus de niveaux de faible complexité avec Hawkes, parce que la connaissance tend à diminuer avec le temps, puis l'algorithme force à renforcer la connaissance dans tous les niveaux de complexité et puisque la configuration initiale donne une plus grande probabilité aux niveaux inférieurs, l'algorithme tend à répéter les niveaux plus accessibles nécessaires pour atteindre les niveaux supérieurs. -\subsection{Base de données simulée (ESCBR, TS avec Hawkes)} +\subsubsection{Base de données simulée (ESCBR, TS avec Hawkes)} La base de données simulée est générée à l'aide d'une distribution log-normale de probabilité pour simuler les notes de 1000 apprenants dans cinq niveaux de complexité, chacun comportant quinze questions. Le générateur simule une plus grande complexité en réduisant la moyenne et en augmentant la variabilité de la distribution de probabilité. @@ -905,7 +905,7 @@ L'évolution de la variance (figure \ref{fig:vars}) montre qu'avec le processus \label{fig:vars} \end{figure} -\section{Conclusion} +\subsection{Conclusion} Ce chapitre a présenté un algorithme intégré entre deux modèles développés précédemment, un système de recommandation fondé sur l'algorithme d'échantillonnage de Thompson, un modèle de régression d'ensemble fondé sur le raisonnement par cas et une simulation de courbe d'oubli en utilisant le processus de Hawkes. L'algorithme intégré est appliqué à un EIAH appelé AI-VT. Les résultats montrent en effet que l'intégration permet d'obtenir des résultats similaires, mais avec un processus plus réaliste, ce qui permet de mieux personnaliser le système et de faciliter l'acquisition de connaissances. diff --git a/main.log b/main.log index 6ae5497..e4883ed 100644 --- a/main.log +++ b/main.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023) (preloaded format=pdflatex 2023.5.31) 21 MAY 2025 15:57 +This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023) (preloaded format=pdflatex 2023.5.31) 27 MAY 2025 16:15 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -1012,10 +1012,10 @@ LaTeX Warning: Label `eqBeta' multiply defined. LaTeX Warning: Label `tabAlgs' multiply defined. -LaTeX Warning: Label `tabvp' multiply defined. +LaTeX Warning: Label `IntEq1' multiply defined. -LaTeX Warning: Label `IntEq1' multiply defined. +LaTeX Warning: Label `tabvp' multiply defined. 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