From 2e662ed514dcd81244f2341ef460529ca0dfd9ef Mon Sep 17 00:00:00 2001 From: dsotofor Date: Thu, 24 Apr 2025 21:58:58 +0200 Subject: [PATCH] another version --- .DS_Store | Bin 10244 -> 10244 bytes Figures/Var.png | Bin 0 -> 103190 bytes Figures/VarH.png | Bin 0 -> 108750 bytes Figures/stabilityBoxplot1.png | Bin 0 -> 22160 bytes Figures/stabilityBoxplot2.png | Bin 0 -> 22154 bytes chapters/Conclusions.aux | 57 ++++ chapters/Conclusions.tex | 29 ++ chapters/ESCBR-SMA.aux | 93 ++++++ chapters/ESCBR-SMA.tex | 293 +++++++++++++++++++ chapters/ESCBR.aux | 24 +- chapters/ESCBR.tex | 50 ++-- chapters/Publications.aux | 57 ++++ chapters/Publications.tex | 27 ++ chapters/TS_ESCBR-SMA-Hawkes.aux | 85 ++++++ chapters/TS_ESCBR-SMA-Hawkes.tex | 180 ++++++++++++ chapters/TS_ESCBR-SMA.aux | 120 ++++++++ chapters/TS_ESCBR-SMA.tex | 388 ++++++++++++++++++++++++ main.aux | 7 +- main.log | 600 ++++++++++++++++++++++++++++++-------- main.out | 33 +++ main.pdf | Bin 6938195 -> 7696851 bytes 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environnement standard réel afin d'obtenir des informations sur certains groupes caractéristiques spécifiques d'étudiants et de comparer les résultats obtenus avec les résultats théoriques, consolidant ainsi les preuves comportementales et l'efficacité du modèle proposé. + +Comme travail futur, il est proposé d'intégrer dans le modèle d'autres variables obtenues avec des algorithmes d'intelligence artificielle complémentaires tels que l'analyse vidéo, l'analyse audio et même l'analyse des données obtenues des apprenants tout au long du processus d'apprentissage. Analyser le modèle avec différentes configurations paramétriques, afin de déterminer quelles sont les configurations les plus appropriées et comment chaque variable influence le comportement global des algorithmes exécutés et le résultat final. + +Comme perspectives de ce travail peuvent être envisagées : +\begin{itemize} + \item L'étude du modèle de raisonnement à partir de cas en profondeur avec l'analyse de changement des paramètres. + \item Analyser le comportement de l'algorithme avec des metriques de distance différentes de la distance Euclidiene. + \item Analyser la modification de la fonction de optimisation associé au choix de la meilleure solution dans les solutions générées par le second stacking processus. + \item Détérminer le point de rupture pour différents scénarios. +\end{itemize} + +Pour l'échantillonage de Thompson les perspectives ouvertes par ce travail sont : +\begin{itemize} + \item Changer la famille des distributions de probabilité et étudier la performace obtenue. + \item Calculer de façon dynamique les taux corrélées d'actualisation des ditributions de probabilité pour chaque niveau de complexité. + \item Ajouter une comportement décroissante à l'actualisation des distributions de probabilité pour améliorer l'adaptabilité su modèle. +\end{itemize} + +Aussi, évaluer le système avec une base de données avec des erreurs pour mesurer la résilience du modèle et comment il peut s'autocorregir face à d'eventuels disfonctionnements. + +De façon générale il est possible de définir des intervales pour chaque paramètre et executer un analyse de sensibilité pour évaluer les résultats avec l'objetif de estimer la stabilité du système et les limites numériques. diff --git a/chapters/ESCBR-SMA.aux b/chapters/ESCBR-SMA.aux new file mode 100644 index 0000000..b700d54 --- /dev/null +++ b/chapters/ESCBR-SMA.aux @@ -0,0 +1,93 @@ +\relax +\providecommand\hyper@newdestlabel[2]{} +\citation{KAMALI2023110242} +\citation{DIDDEN2023338} +\citation{HIPOLITO2023103510} +\citation{ZHANG2023110564} +\citation{10.1007/978-3-031-63646-2_11} +\@writefile{toc}{\contentsline {chapter}{\numberline {8}Intégration du Raisonnement à partir de cas (RàPC) et des Systèmes Multi-Agent (SMA)}{73}{chapter.8}\protected@file@percent } +\@writefile{lof}{\addvspace {10\p@ }} +\@writefile{lot}{\addvspace {10\p@ }} +\@writefile{toc}{\contentsline {section}{\numberline {8.1}Introduction}{73}{section.8.1}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\numberline {8.2}Modèle Proposé}{74}{section.8.2}\protected@file@percent } +\@writefile{lof}{\contentsline {figure}{\numberline {8.1}{\ignorespaces Deux cycles du système ESCBR-SMA proposé\relax }}{74}{figure.caption.46}\protected@file@percent } +\newlabel{figNCBR}{{8.1}{74}{Deux cycles du système ESCBR-SMA proposé\relax }{figure.caption.46}{}} +\@writefile{lot}{\contentsline {table}{\numberline {8.1}{\ignorespaces Variables et paramètres du modèle proposé (Type: p - 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À partir des informations qu'ils perçoivent et échangent, les agents peuvent apprendre de manière autonome et atteindre leurs objectifs de manière efficace \cite{KAMALI2023110242}. Les systèmes multi-agents peuvent être exécutés en parallèle étant donné l'indépendance des agents, ils sont robustes aux problèmes qui présentent une incertitude \cite{DIDDEN2023338}. + +Le raisonnement Bayésien est une hypothèse sur le fonctionnement du cerveau humain et sa relation avec l'environnement, dont le principe est que les expériences passées permettent de déduire les états futurs, ce qui permet d'agir et de prendre des décisions \cite{HIPOLITO2023103510}, également des informations peuvent être deduites et d'apprendre à partir d'informations incomplètes \cite{ZHANG2023110564}. + +Nous proposons ici un modèle qui intègre un algorithme de raisonnement à paritr de cas avec des systèmes multi-agents cognitifs qui utilisent le raisonnement Bayésien afin d'améliorer les processus de recherche de voisins et de génération de solutions en utilisant l'échange d'informations inter-agents et l'apprentissage par renforcement, obtenant ainsi des effets émergents dans le comportement global de l'algorithme, ce qui peut conduire à l'amélioration des prédictions de l'algorithme ESCBR \cite{10.1007/978-3-031-63646-2_11}. + +\section{Modèle Proposé} + +L'algorithme ESCBR-SMA est basé 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}. + +\begin{figure}[!ht] +\centering +\includegraphics[scale=0.65]{Figures/NCBR.png} +\caption{Deux cycles du système ESCBR-SMA proposé} +\label{figNCBR} +\end{figure} + +ESCBR-SMA correspond aux deux étapes de l'ESCBR (Ensemble Stacking Case-Based Reasoning) %\cite{} +intégrées à un système multi-agents. Chaque agent effectue un algorithme de recherche des voisins du problème au cours de la première étape et, au cours de la seconde, génère une solution en se référant à la liste des solutions obtenues au cours de la première étape. À chaque itération, les agents peuvent choisir parmi trois comportements programmés : la recherche de problèmes voisins, la génération de solutions ou l'échange d'informations avec un autre agent. L'exécution asynchrone est employée pour ces comportements, tandis que la création et la sélection de la liste des voisins se font de manière synchrone pour unifier l'algorithme global. La création et la sélection des voisins se font de manière synchrone pour unifier l'algorithme global. + +Les étapes d'extraction, de réutilisation, de révision et de conservation restent conformes au modèle RàPC conventionnel. L'algorithme proposé comprend désormais trois nouvelles étapes. Dans la phase de reconfiguration, les agents mettent à jour les valeurs de leurs paramètres locaux afin d'améliorer la qualité de la solution proposée lors de l'itération suivante. Dans la phase d'échange, les agents échangent des informations pour améliorer leurs processus internes de recherche et de génération. L'étape de rénovation met à jour les valeurs des paramètres globaux de l'algorithme. Le flux complet de l'algorithme proposé est présenté dans la figure \ref{figFlowCBR}, où l'on peut voir que l'algorithme commence par la création de n agents. Lors de l'initialisation, les agents sélectionnent au hasard un algorithme de récupération et un algorithme de réutilisation, et initialisent également les vecteurs bayésiens correspondants. Tous les agents travaillent avec le même ensemble de données. En parallèle, les agents exécutent l'algorithme de récupération sélectionné, à partir des problèmes similaires trouvés, chaque agent extrait les solutions et exécute l'algorithme spécifique de génération d'une nouvelle solution. Toutes les solutions proposées par les agents sont évaluées à l'aide d'une fonction objective de minimisation, c'est-à-dire que la solution qui minimise la fonction objective est la meilleure solution possible. Au cours de l'étape suivante, les agents sélectionnent au hasard un algorithme de récupération et un algorithme de réutilisation, puis mettent à jour les vecteurs bayésiens en fonction des résultats obtenus avec la fonction objective. Lors de l'itération suivante, chaque agent peut choisir l'une des trois actions possibles : changer les algorithmes de récupération et de réutilisation, ne changer que l'algorithme de réutilisation ou échanger des informations avec un autre agent choisi au hasard. Le choix aléatoire d'une action différente permet à l'agent de construire et d'améliorer une solution candidate. + +Les variables et paramètres complets de l'algorithme proposé sont présentés dans le tableau \ref{tabVarPar}. Le système multi-agents est composé d'un nombre variable d'agents, tous homogènes mais dotés de processus cognitifs internes indépendants et stochastiques. + +\begin{figure}[!ht] +\centering +\includegraphics[scale=0.6]{Figures/FlowCBR.png} +\caption{Flux du \textit{Stacking} du RàPC (* est une tâche effectuée par chaque agent)} +\label{figFlowCBR} +\end{figure} + +\begin{table}[!ht] +\footnotesize +\centering +\begin{tabular}{cccc} +ID&Type&Description&Domain\\ +\hline +$it$&p&Nombre d'itérations&$\mathbb{N}, it>0$\\ +$np$&p&Nombre d'agents&$\mathbb{N}, np>2$\\ +$nl$&p&Nombre maximal de voisins locaux&$\mathbb{N}, nl>0$\\ +$ng$&p&Nombre de voisins globaux&$\mathbb{N}, ng>2$\\ +$n$&v&Dimension de l'espace du problème&$\mathbb{N}, n>0$\\ +$m$&v&Dimension de l'espace de solution&$\mathbb{N}, m>0$\\ +$p$&v&Description du problème&$\mathbb{R} ^ n$\\ +$s$&v&Description de la solution&$\mathbb{R} ^ m$\\ +$p_w$&v&Description du nouveau problème&$\mathbb{R} ^ n$\\ +$s_w$&v&Description de la nouvelle solution&$\mathbb{R} ^ m$\\ +$n_{rt}$&v&Nombre d'algorithmes por l'étape de rétrouver&$\mathbb{Z}$\\ +$n_{rs}$&v&Nombre d'algorithmes de réutilisation&$\mathbb{Z}$\\ +$d(x_1,x_2)$&f&Fonction de distance entre $x_1$ et $x_2$ &$\mathbb{R}$\\ +$rn(x,y)$&f& + +\begin{tabular}{@{}c@{}}Valeur aléatoire avec distribution normale\\ $x$ moyenne, $y$ écart-type +\end{tabular} + +&$\mathbb{R}_+$\\ +$rnp(x,y)$&f& + +\begin{tabular}{@{}c@{}}Valeur aléatoire discrète, $x$ nombre d'options \\ $y$ vecteur discret de probabilités +\end{tabular} +&$\mathbb{Z}$\\ +$f_s(p^n,s^m)$&f&Évaluation des solutions&$\mathbb{R}$\\ +\end{tabular} +\caption{Variables et paramètres du modèle proposé (Type: p - paramètre, v - variable, f - fonction)} +\label{tabVarPar} +\end{table} + +\subsection{Algorithmes} +Lors de la première étape de l'empilage, chaque agent peut sélectionner l'un des algorithmes mis en Å“uvre 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 basé 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 basé sur le vote copie l'information la plus fréquente entre les solutions. L'algorithme basé 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} + +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. + +Il y a trois actions possibles à exécuter (« Récupérer et réutiliser », « Réutiliser » et « Échanger ») et huit variables : le nombre de voisins qui définit le nombre de problèmes similaires au nouveau problème posé que l'agent doit rechercher dans la base de données, la liste des voisins les plus proches établit la liste des agents voisins avec lesquels des informations peuvent être échangées, l'algorithme de récupération est l'identifiant de l'algorithme que l'agent va exécuter pour trouver les problèmes similaires au nouveau problème, l'algorithme de réutilisation est l'identifiant de l'algorithme que l'agent va exécuter pour générer une solution candidate au nouveau problème, solution est la description de la solution générée, évaluation de la solution est la valeur numérique décrivant la qualité de la solution générée selon une fonction d'optimisation (eq \ref{eqOpt1} et eq \ref{eqOpt2}), vecteur bayésien pour les algorithmes de récupération contenant les valeurs de probabilité pour chacun des algorithmes de récupération et vecteur bayésien pour les algorithmes de réutilisation contenant les valeurs de probabilité pour chacun des algorithmes de réutilisation. + +\begin{equation} +min \; \left( f_s(p_w^n, s_w^m) \right) = min \left( \sum_{i=1}^{ng} \frac{d(s_w^m,s_i^t)}{d(p_w^n,p_i^n)^2} \right) +\label{eqOpt1} +\end{equation} + +\begin{equation} +s_i^t=s_i^m+rn(0,d(p_w^n,p_i^n)) +\label{eqOpt2} +\end{equation} + +\begin{figure}[!ht] +\centering +\includegraphics[scale=0.7]{Figures/agent.png} +\caption{Structure interne des agents} +\label{figAgent} +\end{figure} + +\subsection{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. + +L'apprentissage est basé sur un raisonnement bayésien où les vecteurs de récupération et de réutilisation sont initialisés avec une probabilité uniforme pour tous les algorithmes, comme le montre la figure \ref{fig:bayev}. Au cours d'une itération, si un algorithme a contribué à la construction de la meilleure solution, il reçoit un point pour chaque agent qui l'a utilisé. Ces informations sont stockées dans un vecteur normalisé qui est ensuite utilisé comme vecteur de vraisemblance $P(A)$ pour calculer les nouvelles probabilités dans l'équation bayésienne \ref{eqBay}, $P(B)$ est le terme de normalisation global. + +\begin{figure} + \centering + \includegraphics[scale=0.5]{Figures/BayesianEvolution.png} + \caption{Exemple d'évolution Bayésienne des vecteurs pour un agent. a) Initialisation des probabilités $P(B|A)$ vecteurs pour Retrieve et Reuse, b) Probabilités après quelques itérations $P(A|B)$ vecteurs pour Retrieve et Reuse} + \label{fig:bayev} +\end{figure} + +\begin{equation} + P(A|B)=\frac{P(B|A)P(A)}{P(B)} + \label{eqBay} +\end{equation} + +La sélection d'un algorithme de recherche $a_{rt}$ se fait au moyen d'une valeur aléatoire tirée du vecteur de distribution de recherche discrète obtenu par raisonnement bayésien, comme le montre l'équation \ref{eqRta}. + +\begin{equation} + a_{rt}=rnp(n_{rt},P(A|B)_{rt}) + \label{eqRta} +\end{equation} + +La sélection d'un algorithme de réutilisation $a_{rs}$ se fait au moyen d'une valeur aléatoire tirée du vecteur de distribution de réutilisation discrète obtenu par raisonnement bayésien, comme le montre l'équation \ref{eqRsa}. + +\begin{equation} + a_{rs}=rnp(n_{rs},P(A|B)_{rs}) + \label{eqRsa} +\end{equation} + +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} + +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} + +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}. + +\begin{table}[!ht] +\footnotesize +\centering +\begin{tabular}{c|ccccccccccc} +&A1&A2&A3&A4&A5&A6&A7&A8&A9&A10\\ +\hline +%DS1&9.081&12.301&1.228&1.066&7.763&9.081&9.078&9.764&0.750&8.263&8.225\\ +DS1&9.081&12.301&1.228&1.066&7.763&9.081&9.078&9.764&0.750&8.225\\ +%DS2&0.022&0.025&0.019&0.013&0.017&0.022&0.022&0.037&0.011&0.016&0.016\\ +DS2&0.022&0.025&0.019&0.013&0.017&0.022&0.022&0.037&0.011&0.016\\%DS3&8.756&8.465&9.656&7.665&8.716&8.756&9.005&9.177&7.369&8.148&7.991\\ +DS3&8.756&8.465&9.656&7.665&8.716&8.756&9.005&9.177&7.369&7.991\\ +%DS4&0.647&0.752&0.794&0.602&0.688&0.647&0.646&0.798&0.616&0.628&0.607\\ +DS4&0.647&0.752&0.794&0.602&0.688&0.647&0.646&0.798&0.616&0.607\\ +%DS5&0.767&0.824&0.877&0.66&0.826&0.767&0.775&0.87&0.703&0.690&0.662\\ +DS5&0.767&0.824&0.877&0.66&0.826&0.767&0.775&0.87&0.703&0.662\\ +%DS6&10.525&9.174&6.93&5.372&6.662&10.525&10.525&10.527&5.131&9.413&9.070\\ +DS6&10.525&9.174&6.93&5.372&6.662&10.525&10.525&10.527&5.131&9.070\\ +%DS7&2.961&2.451&0.589&0.528&3.955&2.961&3.009&4.083&0.490&3.031&2.941\\ +DS7&2.961&2.451&0.589&0.528&3.955&2.961&3.009&4.083&0.490&2.941\\ +%DS8&1.298&1.125&1.360&1.197&1.486&1.298&1.298&1.306&1.128&2.752&2.553\\ +DS8&1.298&1.125&1.360&1.197&1.486&1.298&1.298&1.306&1.128&2.553\\ +%DS9&2.256&2.565&3.174&2.377&2.817&2.256&2.255&2.468&2.293&2.747&2.468\\ +DS9&2.256&2.565&3.174&2.377&2.817&2.256&2.255&2.468&2.293&2.468\\ +%DS10&3.136&3.415&4.173&3.165&3.710&3.136&3.135&3.161&3.108&3.897&3.621\\ +DS10&3.136&3.415&4.173&3.165&3.710&3.136&3.135&3.161&3.108&3.621\\ +DS11&0.625&0.565&0.741&0.56&0.606&0.626&0.626&0.681& +0.541&0.54\\ +\hline +%Avg. Rank&5.8&6.5&7.2&2.3&6.7&5.7&5.6&8.65&1.9&4.65\\ +Avg. Rank&6.4&6.9&8.2&2.6&7.2&6.45&6.35&9.55&2.1&4.75\\ +\end{tabular} +\caption{Résultat de la métrique RMSE (Root Mean Squared Error) pour les bases de données évaluées avec des algorithmes de régression} +\label{tabRes1} +\end{table} + +\begin{table}[!ht] +\scriptsize +\centering +\begin{tabular}{llccp{1.4cm}p{1.2cm}p{1.2cm}} +ID&DataSet&Features&Instances&Output. Dimension&Input. Domain&Output Domain\\ +\hline +DS1&Yatch Hydrodynamics&6&308&1&$\mathbb{R}$&$\mathbb{R}$\\ +DS2&Electrical Grid Stability&12&10000&1&$\mathbb{R}$&$\mathbb{R}$\\ +DS3&Real State Valuation&6&414&1&$\mathbb{R_+}$&$\mathbb{R_+}$\\ +DS4&Wine Quality (Red)&11&1598&1&$\mathbb{R_+}$&$\mathbb{N}$\\ +DS5&Wine Quality (White)&11&4897&1&$\mathbb{R_+}$&$\mathbb{N}$\\ +DS6&Concrete Compressive Strength&8&1030&1&$\mathbb{R_+}$&$\mathbb{R_+}$\\ +DS7&Energy Efficiency&8&768&2&$\mathbb{R_+}$&$\mathbb{R_+}$\\ +DS8&Gas Turbine CO, NOx Emission (2015)&9&7384&2&$\mathbb{R_+}$&$\mathbb{R_+}$\\ +DS9&Student Performace Portuguese&30&649&3&$\mathbb{N*}$&$\mathbb{N}$\\ +DS10&Student Performance Math&30&395&3&$\mathbb{N*}$&$\mathbb{N}$\\ +DS11&Generated Student Performance&5&1000&1&$\mathbb{R}_+$&$\mathbb{R}_+$\\ +\end{tabular} +\caption{Description des bases de données évaluées. (* après codification comme +\textit{String})} +\label{tabBases} +\end{table} + +\begin{table}[!ht] +\centering +\begin{tabular}{ccc|ccc} +ID&Parameter&Value&ID&Parameter&Value\\ +\hline +A1&Intercept&True&A6&Degree&4\\ +&Positive&True&&Bias&True\\ +\hline +A2&Neighbors&5&A7&Fit Intercept&True\\ +&Weights&Uniform&&alpha&0.2\\ +&Metric&Minkowsky&&tol&1e-4\\ +&Power Minkowsky&2\\ +\hline +A3&Error&Squared Error&A8&Fit Intercept&True\\ +&Min samples split&2&&alpha&[0.00001, 0.4]\\ +&&&&Max iter&1000\\ +&&&&tol&1e-4\\ +\hline +A4&Estimators&10&A9&Error&Squarred Error\\ +&Error&Squared Error&&Learning Rate&0.1\\ +&Min samples split&2&&Estimators&100\\ +&Bootstrap&True&&Min Split&2\\ +\hline +A5&Hidden Layers&100\\ +&Activation&Relu\\ +&Solver&Adam\\ +&alpha&0.0001\\ +&Learning Rate&0.001\\ +&Max Iter&200\\ +&beta1&0.9\\ +&beta2&0.999\\ +&epsilon&1e-8\\ +\end{tabular} +\caption{Paramètres pour tous les algorithmes comparés} +\label{AlgsPar} +\end{table} + +Le classement moyen de toutes les bases de données en fonction de la mesure RMSE (Root Mean Square Error) est indiqué dans le tableau \ref{tabRes1}. Les résultats détaillés des mêmes algorithmes et des mêmes bases de données, mais comparés avec la métrique MAE (Median Absolute Error), sont présentés dans le tableau \ref{tabRes2}. + +\begin{table}[!ht] +\footnotesize +\centering +\begin{tabular}{c|ccccccccccc} +Dataset&A1&A2&A3&A4&A5&A6&A7&A8&A9&A10\\ +\hline +%DS1&6.776&2.385&0.231&0.207&3.632&6.778&6.307&5.186&0.162&1.193&1.218\\ +DS1&6.776&2.385&0.231&0.207&3.632&6.778&6.307&5.186&0.162&1.218\\ +%DS2&0.015&0.017&0.012&0.008&0.012&0.015&0.015&0.030&0.007&0.011&0.010\\ +DS2&0.015&0.017&0.012&0.008&0.012&0.015&0.015&0.030&0.007&0.010\\ +%DS3&5.092&4.320&4.1&3.632&4.435&5.092&5.20&5.132&3.504&3.90&3.771\\ +DS3&5.092&4.320&4.1&3.632&4.435&5.092&5.20&5.132&3.504&3.771\\ +%DS4&0.413&0.495&0.18&0.325&0.451&0.413&0.412&0.544&0.387&0.154&0.135\\ +DS4&0.413&0.495&0.18&0.325&0.451&0.413&0.412&0.544&0.387&0.135\\ +%DS5&0.509&0.548&0.285&0.374&0.550&0.509&0.509&0.633&0.456&0.113&0.085\\ +DS5&0.509&0.548&0.285&0.374&0.550&0.509&0.509&0.633&0.456&0.085\\ +%DS6&6.989&5.709&3.134&2.839&4.306&6.989&6.989&6.986&3.084&5.439&5.072\\ +DS6&6.989&5.709&3.134&2.839&4.306&6.989&6.989&6.986&3.084&5.072\\ +%DS7&1.393&1.372&0.217&0.218&2.523&1.393&1.529&2.346&0.243&1.008&1.006\\ +DS7&1.393&1.372&0.217&0.218&2.523&1.393&1.529&2.346&0.243&1.006\\ +%DS8&0.549&0.297&0.365&0.289&0.742&0.549&0.549&0.540&0.309&0.861&0.794\\ +DS8&0.549&0.297&0.365&0.289&0.742&0.549&0.549&0.540&0.309&0.794\\ +%DS9&1.496&1.788&2.080&1.612&2.005&1.496&1.496&1.714&1.538&1.721&1.556\\ +DS9&1.496&1.788&2.080&1.612&2.005&1.496&1.496&1.714&1.538&1.556\\ +%DS10&2.344&2.534&2.910&2.331&2.543&2.344&2.344&2.481&2.258&2.602&2.371\\ +DS10&2.344&2.534&2.910&2.331&2.543&2.344&2.344&2.481&2.258&2.371\\ +DS11&0.387&0.35&0.46&0.338&0.384&0.387&0.387&0.453& +0.327&0.347\\ +\hline +Avg. Rank&7.15&6.9&5.35&2.6&7.95&7.25&7.3&9.0&2.5 +&4.5\\ +%Avg. Rank&6.45&6.5&4.35&2.4&7.45&6.55&6.6&8.1&2.4&4.2\\ +\end{tabular} +\caption{Comparaison des résultats MAE (Median Absolute Error) pour les bases de données évaluées avec des algorithmes de régression} +\label{tabRes2} +\end{table} + +La dispersion globale, la médiane et les valeurs aberrantes pour toutes les bases données évaluées sont présentées dans la figure \ref{figBox}, où l'on peut voir que l'algorithme proposé génère dans certains cas plus de valeurs aberrantes que d'autres algorithmes, mais la variance est très faible et la convergence est proche de la valeur réelle, meilleure que la plupart des algorithmes comparés. Les valeurs aberrantes sont plus élevées que les valeurs réelles. + +\begin{figure}[!ht] +\includegraphics[scale=0.26]{Figures/boxplot2.png} +\caption{Résultats de la métrique MAE (Median Absolute Error) pour dix algorithmes} +\label{figBox} +\end{figure} + +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} +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. 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Une partie du contenu est extrait et traduit de l’article Soto \textit{et al.} \cite{10.1007/978-3-031-63646-2_11}.\\ +Ce chapitre présente un modèle basé sur le raisonnement à partir de cas et les méthodes d'ensemble avec un double empilement itératif en deux étapes pour trouver des solutions approximatives à des problèmes de régression unidimensionnels et multidimensionnels. Une partie du contenu est extrait et traduit de l’article Soto \textit{et al.} \cite{10.1007/978-3-031-63646-2_11}. -Cette approche ne nécessite pas d'entrainement, et peut fonctionner avec des données dynamiques au moment de l'exécution. Les solutions sont générées à l'aide d'algorithmes stochastiques afin de permettre l'exploration de l'espace des solutions, l'évaluation est effectuée en transformant le problème de régression en un problème d'optimisation avec une fonction objectif associée. L'algorithme a été testé en comparaison avec neuf algorithmes de régression classiques sur dix bases de données de régression différentes extraites du site de l'UCI, les résultats montrent que l'algorithme proposé génère dans la plupart des cas des solutions assez proches des solutions réelles, selon le RMSE l'algorithme se trouve globalement parmi les six meilleurs algorithmes et avec MAE au troisième meilleur algorithmes des dix évalués, suggérant que les résultats sont raisonnablement bons.\\ +Cette approche ne nécessite pas d'entrainement, et peut fonctionner avec des données dynamiques au moment de l'exécution. Les solutions sont générées à l'aide d'algorithmes stochastiques afin de permettre l'exploration de l'espace des solutions, l'évaluation est effectuée en transformant le problème de régression en un problème d'optimisation avec une fonction objectif associée. L'algorithme a été testé en comparaison avec neuf algorithmes de régression classiques sur dix bases de données de régression différentes extraites du site de l'UCI, les résultats montrent que l'algorithme proposé génère dans la plupart des cas des solutions assez proches des solutions réelles, selon le RMSE l'algorithme se trouve globalement parmi les six meilleurs algorithmes et avec MAE au troisième meilleur algorithmes des dix évalués, suggérant que les résultats sont raisonnablement bons. -Les méthodes d'ensemble utilisent plusieurs modèles multiples exécutés indépendamment et leurs résultats sont combinés pour obtenir une prédiction globale finale. L'idée principale est d'améliorer les résultats et la capacité de généralisation des modèles individuels. Certaines méthodes d'ensemble utilisent différents modèles avec différents ensembles de données, d'autres utilisent les mêmes modèles avec des paramètres différents, la combinaison des résultats des multiples modèles peut utiliser différentes stratégies comme des règles simples ou des approches plus complexes \cite{BAKUROV2021100913}. Les méthodes d'ensemble sont utiles dans les problèmes de classification et de régression.\\ +Les méthodes d'ensemble utilisent plusieurs modèles multiples exécutés indépendamment et leurs résultats sont combinés pour obtenir une prédiction globale finale. L'idée principale est d'améliorer les résultats et la capacité de généralisation des modèles individuels. Certaines méthodes d'ensemble utilisent différents modèles avec différents ensembles de données, d'autres utilisent les mêmes modèles avec des paramètres différents, la combinaison des résultats des multiples modèles peut utiliser différentes stratégies comme des règles simples ou des approches plus complexes \cite{BAKUROV2021100913}. Les méthodes d'ensemble sont utiles dans les problèmes de classification et de régression. Les méthodes d'apprentissage automatique appliquées à la régression permettent de prédire des valeurs pour différents types de problèmes en construisant, évaluant et formant des modèles linéaires et non linéaires complexes, mais s'il est possible d'améliorer la précision en les intégrant, les stratégies d'intégration les plus courantes utilisées pour l'apprentissage d'ensemble sont les suivantes : Stacking, Boosting et Bagging \cite{Liang}. Le Stacking est un type de méta-modèle d'apprentissage profond d'ensemble, dont l'objectif est d'utiliser diverses techniques d'apprentissage automatique pour surmonter les limites des modèles individuels, l'intégration générant un résultat final avec une précision améliorée \cite{cmc.2023.033417}. Dans les méthodes d'empilage, les algorithmes de base sont appelés niveau-0, il s'agit généralement de modèles ou d'algorithmes d'apprentissage automatique hétérogènes qui travaillent tous avec la même base de données. Le méta-algorithme qui unifie les résultats peut être une autre technique d'apprentissage automatique ou un ensemble de règles qui reçoit comme données d'entrée les résultats des algorithmes de niveau-0 est appelé niveau-1 \cite{10.3389/fgene.2021.600040}. \section{Modèle Proposé} -L'algorithme proposé ESCBR (Ensemble Stacking Case-Based Reasoning) est basé sur le paradigme générique CBR avec plusieurs algorithmes de recherche de voisins et de génération de solutions qui ont été intégrés selon une variation du modèle de stacking en deux étapes itératives, cette intégration donne à l'algorithme la capacité de s'adapter à différents types de problèmes, d'éviter les biais et le surentraînement. 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}.\\ +L'algorithme proposé ESCBR (Ensemble Stacking Case-Based Reasoning) est basé sur le paradigme générique CBR avec plusieurs algorithmes de recherche de voisins et de génération de solutions qui ont été intégrés selon une variation du modèle de stacking en deux étapes itératives, cette intégration donne à l'algorithme la capacité de s'adapter à différents types de problèmes, d'éviter les biais et le surentraînement. 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}. \begin{figure}[!ht] \centering @@ -60,7 +60,7 @@ $f_s(p^n,s^m)$&f&Évaluation des solutions&$\mathbb{R}$\\ \end{table} \subsection{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 Å“uvre pour l'étape de récupération : KNN (K Nearest Neighbors), KMeans, GMM (Gaussian Mixture Model), FuzzyC et KNN Ponderation.\\ +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 Å“uvre pour l'étape de récupération : KNN (K Nearest Neighbors), KMeans, GMM (Gaussian Mixture Model), FuzzyC et KNN Ponderation. \begin{figure} \centering @@ -73,7 +73,7 @@ Formellement, le premier modèle de stacking proposé fonctionne avec deux param \subsection{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 Å“uvre 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.\\ +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 Å“uvre 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. \begin{figure}[!ht] \centering @@ -82,7 +82,7 @@ Une fois la liste globale des cas similaires établie, les informations correspo \label{figAuto} \end{figure} -La moyenne pondérée avec probabilité permet de construire une solution selon le calcul de la moyenne avec le poids de chaque solution en fonction de sa proximité au nouveau problème. L'équation \ref{gen00} define le calcul de la probabilité en fonction de la distance entre les problèmes et l'équation \ref{gen01} construit la solution en calculant chaque case $j$.\\ +La moyenne pondérée avec probabilité permet de construire une solution selon le calcul de la moyenne avec le poids de chaque solution en fonction de sa proximité au nouveau problème. L'équation \ref{gen00} define le calcul de la probabilité en fonction de la distance entre les problèmes et l'équation \ref{gen01} construit la solution en calculant chaque case $j$. \begin{equation} \alpha_j=\frac{d(p_j^n,p_w^n)}{\sum_{i=0}^{nl} d(p_i^n,p_w^n)} @@ -94,14 +94,14 @@ La moyenne pondérée avec probabilité permet de construire une solution selon \label{gen01} \end{equation} -La moyenne sans probabilité copie aléatoirement les informations des solutions selon la distribution uniforme en donnant la même probabilité à toutes les elements de toutes les solutions proches. Formellement la génération de la solution est écrite commme l'equation \ref{gen2}, où chaque position $j$ est calculée de la même façon.\\ +La moyenne sans probabilité copie aléatoirement les informations des solutions selon la distribution uniforme en donnant la même probabilité à toutes les éléments de toutes les solutions proches. Formellement la génération de la solution est écrite comme l'équation \ref{gen2}, où chaque position $j$ est calculée de la même façon. \begin{equation} s^m_{w,j}= \frac{1}{nl} \sum_{i=0}^{nl} s_{i,j} \label{gen2} \end{equation} -La génération de la solution par valeurs médianes construit la solution en utilisant la valeur médiane de toutes les solutions pour chaque dimension.\\ +La génération de la solution par valeurs médianes construit la solution en utilisant la valeur médiane de toutes les solutions pour chaque dimension. \begin{equation} s_{w,j}^m= @@ -111,7 +111,7 @@ La génération de la solution par valeurs médianes construit la solution en ut \end{cases} \end{equation} -La sélection aleatoire avec probabilité génére une solution en copiant aléatoirement l'information des solutions dans chaque position ayant une plus grande probabilité vers le cas de problème associé le plus proche.\\ +La sélection aléatoire avec probabilité génère une solution en copiant aléatoirement l'information des solutions dans chaque position ayant une plus grande probabilité vers le cas de problème associé le plus proche. \begin{equation} s_{w,k}^m=max(P(S_j))_k \; with \; probability \; \alpha_j \; \forall k=\{1,...,m\} @@ -119,31 +119,31 @@ s_{w,k}^m=max(P(S_j))_k \; with \; probability \; \alpha_j \; \forall k=\{1,..., \textcolor{red}{complete all the models formalization...} -Copie/changement, copie les informations d'une solution aléatoire et change une partie avec les informations d'une autre solution sélectionnée aléatoirement.\\ +Copie/changement, copie les informations d'une solution aléatoire et change une partie avec les informations d'une autre solution sélectionnée aléatoirement. \begin{equation} s_{w}^m=max(P(S_j)) \; with \; uniform \; probability \end{equation} -Le vote permet de copier l'information qui se présente avec plus de fréquence entre toutes les solutions.\\ +Le vote permet de copier l'information qui se présente avec plus de fréquence entre toutes les solutions. \begin{equation} s_{w,j}^m=max(\#(s_{j})) \end{equation} -L'interpolation utilise des informations aléatoires à partir d'une fonction d'interpolation lineaire 1D calculée.\\ +L'interpolation utilise des informations aléatoires à partir d'une fonction d'interpolation lineaire 1D calculée. \begin{equation} s_{w,j}^m=rand \left( \left( \frac{y_i-y_{i+1}}{x_i-x_{i+1}} \right) (x-x_i)+y_i \right), \forall i \; | \; 0 \le i < nl \end{equation} -Avec PCA, la description du problème est transformée dans l'espace de description des solutions pour établir une relation entre le problème et sa solution, avec le problème et la solution dans le même espace est calcule la moyenne de la distance entre tous les paires problème-solution et en utilisant la description du nouveau problème et la valeur moyenne de distance une solution est générée.\\ +Avec PCA, la description du problème est transformée dans l'espace de description des solutions pour établir une relation entre le problème et sa solution, avec le problème et la solution dans le même espace est calcule la moyenne de la distance entre tous les paires problème-solution et en utilisant la description du nouveau problème et la valeur moyenne de distance une solution est générée. \begin{equation} s_{w,j}^m= \end{equation} -Marche aléatoire choisit une solution et change les valeurs dans une dimension aléatoirement avec un petit pas. Le petit pas est une valeur aléatoire générée avec une distribution de probabilité normal.\\ +Marche aléatoire choisit une solution et change les valeurs dans une dimension aléatoirement avec un petit pas. Le petit pas est une valeur aléatoire générée avec une distribution de probabilité normal. \begin{equation} s_{w,j}^m=\begin{cases} @@ -168,9 +168,9 @@ Le deuxième modèle de stacking fonctionne avec la description des solutions $s \subsection{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.\\ +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. -La fonction objectif \ref{eqOpt} établi un rapport entre la distance de la solution générée $s^m_w$ et les $x$ solutions connues $s^m_x$ avec un facteur aléatoire de \textit{drift} ainsi que la distance du problème nouveau $p^n_w$ et les $x$ problèmes connus $p^n_w$. Ici, la complexité de trouver le point optimal se trouve dans le fait que tous les points dans l'espace ne sont pas valides comme solution du nouveau problème, c'est la raison pour laquelle le point doit être généré en utilisant l'information des solutions connues. L'objetif de faire ça est de utiliser l'information disponible qui décrit un problème et sa solution pour valider et générer l'ensemble de solutions proposées.\\ +La fonction objectif \ref{eqOpt} établi un rapport entre la distance de la solution générée $s^m_w$ et les $x$ solutions connues $s^m_x$ avec un facteur aléatoire de \textit{drift} ainsi que la distance du problème nouveau $p^n_w$ et les $x$ problèmes connus $p^n_w$. Ici, la complexité de trouver le point optimal se trouve dans le fait que tous les points dans l'espace ne sont pas valides comme solution du nouveau problème, c'est la raison pour laquelle le point doit être généré en utilisant l'information des solutions connues. L'objectif de faire ça est de utiliser l'information disponible qui décrit un problème et sa solution pour valider et générer l'ensemble de solutions proposées. \begin{equation} \lambda_x(p_w, s_w) = \left( \frac{d(s_w^m,(s_x^m+rn(0,d(p_w^n, p_i^n))))}{d(p_w^n,p_x^n)^2} \right) @@ -197,7 +197,7 @@ L'étape de rétention consiste simplement à prendre la meilleure solution prop \section{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 $ng=10$.\\ +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 $ng=10$. \begin{table}[!ht] \tiny @@ -220,7 +220,7 @@ DS10&Student Performance Math&30&395&3&$\mathbb{N*}$&$\mathbb{N}$\\ \label{tabBases} \end{table} -L'algorithme proposé est comparé à neuf algorithmes de régression bien connus et largement utilisés dans divers travaux de recherche et problèmes appliqués. La liste des algorithmes est présentée dans le tableau \ref{tabAlgs}. Tous les algorithmes ont été exécutés 100 fois, et les algorithmes qui nécessitent un entraînement et des validations croisées sont exécutés avec $k=10$.\\ +L'algorithme proposé est comparé à neuf algorithmes de régression bien connus et largement utilisés dans divers travaux de recherche et problèmes appliqués. La liste des algorithmes est présentée dans le tableau \ref{tabAlgs}. Tous les algorithmes ont été exécutés 100 fois, et les algorithmes qui nécessitent un entraînement et des validations croisées sont exécutés avec $k=10$. \begin{table}[!ht] \centering @@ -238,7 +238,7 @@ A5&Multi Layer Perceptron&A10&Proposed Case Based Reasoning\\ \label{tabAlgs} \end{table} -Le tableau \ref{tabRes1} présente le classement moyen de toutes les bases de données en fonction de l'erreur quadratique moyenne (RMSE). Les résultats détaillés des mêmes algorithmes et des mêmes bases de données, mais comparés avec la métrique MAE (Median Absolute Error), sont présentés dans le tableau \ref{tabRes2}.\\ +Le tableau \ref{tabRes1} présente le classement moyen de toutes les bases de données en fonction de l'erreur quadratique moyenne (RMSE). Les résultats détaillés des mêmes algorithmes et des mêmes bases de données, mais comparés avec la métrique MAE (Median Absolute Error), sont présentés dans le tableau \ref{tabRes2}. \begin{table}[!ht] \footnotesize @@ -296,16 +296,16 @@ La dispersion globale, la médiane et les valeurs aberrantes pour quatre bases d \section{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.\\ +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. -On constate également que l'intégration des algorithmes de recherche produit de meilleurs résultats que les algorithmes simples, comme dans le cas de l'algorithme proposé par rapport au KNN ou par rapport à la régression linéaire, bien que pour l'algorithme proposé, l'impact du premier et du deuxième empilement sur les résultats finaux obtenus n'ait pas été déterminé avec précision.\\ +On constate également que l'intégration des algorithmes de recherche produit de meilleurs résultats que les algorithmes simples, comme dans le cas de l'algorithme proposé par rapport au KNN ou par rapport à la régression linéaire, bien que pour l'algorithme proposé, l'impact du premier et du deuxième empilement sur les résultats finaux obtenus n'ait pas été déterminé avec précision. -Globalement, pour le RMSE, les algorithmes de boosting sont plus performants que les algorithmes classiques, même si les performances sont variables. L'algorithme proposé obtient des valeurs acceptables dans toutes les bases de données. D'après la moyenne des positions de classement, pour le RMSE, il est placé à la sixième place, pour le MAE, l'algorithme obtient la meilleure valeur dans trois des dix bases de données et il est placé globalement à la troisième place.\\ +Globalement, pour le RMSE, les algorithmes de boosting sont plus performants que les algorithmes classiques, même si les performances sont variables. L'algorithme proposé obtient des valeurs acceptables dans toutes les bases de données. D'après la moyenne des positions de classement, pour le RMSE, il est placé à la sixième place, pour le MAE, l'algorithme obtient la meilleure valeur dans trois des dix bases de données et il est placé globalement à la troisième place. -Un aspect important de l'algorithme proposé est la fonction objective, qui peut être évaluée et modifiée dynamiquement en fonction des caractéristiques du problème évalué, étant donné que dans la présente étude les tests ont été effectués avec la fonction intuitive qui fournit une plus grande probabilité de sélection et d'évolution à la solution associée aux voisins les plus proches, mais il est possible de compléter l'évaluation avec d'autres termes pertinents et d'améliorer ainsi les résultats.\\ +Un aspect important de l'algorithme proposé est la fonction objective, qui peut être évaluée et modifiée dynamiquement en fonction des caractéristiques du problème évalué, étant donné que dans la présente étude les tests ont été effectués avec la fonction intuitive qui fournit une plus grande probabilité de sélection et d'évolution à la solution associée aux voisins les plus proches, mais il est possible de compléter l'évaluation avec d'autres termes pertinents et d'améliorer ainsi les résultats. 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} -Ce chapitre propose une technique de régression générique utilisant le raisonnement basé 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.\\ +Ce chapitre propose une technique de régression générique utilisant le raisonnement basé 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. diff --git a/chapters/Publications.aux b/chapters/Publications.aux new file mode 100644 index 0000000..317d8a6 --- /dev/null +++ b/chapters/Publications.aux @@ -0,0 +1,57 @@ +\relax +\providecommand\hyper@newdestlabel[2]{} +\@writefile{toc}{\contentsline {chapter}{\numberline {12}Publications}{105}{chapter.12}\protected@file@percent } +\@writefile{lof}{\addvspace {10\p@ }} +\@writefile{lot}{\addvspace {10\p@ }} +\@writefile{toc}{\contentsline {section}{\numberline {12.1}Publications par rapport au sujet de thèse}{105}{section.12.1}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\numberline {12.2}Autres publications}{106}{section.12.2}\protected@file@percent } +\@setckpt{./chapters/Publications}{ +\setcounter{page}{107} +\setcounter{equation}{0} +\setcounter{enumi}{0} +\setcounter{enumii}{0} +\setcounter{enumiii}{0} +\setcounter{enumiv}{0} +\setcounter{footnote}{0} +\setcounter{mpfootnote}{0} +\setcounter{part}{3} +\setcounter{chapter}{12} +\setcounter{section}{2} +\setcounter{subsection}{0} +\setcounter{subsubsection}{0} +\setcounter{paragraph}{0} +\setcounter{subparagraph}{0} +\setcounter{figure}{0} +\setcounter{table}{0} +\setcounter{caption@flags}{2} +\setcounter{continuedfloat}{0} +\setcounter{subfigure}{0} +\setcounter{subtable}{0} +\setcounter{parentequation}{0} +\setcounter{thmt@dummyctr}{0} +\setcounter{vrcnt}{0} +\setcounter{upm@subfigure@count}{0} +\setcounter{upm@fmt@mtabular@columnnumber}{0} +\setcounter{upm@format@section@sectionlevel}{1} +\setcounter{upm@fmt@savedcounter}{0} +\setcounter{@@upm@fmt@inlineenumeration}{0} +\setcounter{@upm@fmt@enumdescription@cnt@}{0} +\setcounter{upmdefinition}{0} +\setcounter{section@level}{1} +\setcounter{Item}{0} +\setcounter{Hfootnote}{0} +\setcounter{bookmark@seq@number}{89} +\setcounter{DefaultLines}{2} +\setcounter{DefaultDepth}{0} +\setcounter{L@lines}{3} +\setcounter{L@depth}{0} +\setcounter{float@type}{8} +\setcounter{algorithm}{1} +\setcounter{ALG@line}{8} +\setcounter{ALG@rem}{8} +\setcounter{ALG@nested}{0} +\setcounter{ALG@Lnr}{2} +\setcounter{ALG@blocknr}{10} +\setcounter{ALG@storecount}{0} +\setcounter{ALG@tmpcounter}{0} +} diff --git a/chapters/Publications.tex b/chapters/Publications.tex new file mode 100644 index 0000000..6d66384 --- /dev/null +++ b/chapters/Publications.tex @@ -0,0 +1,27 @@ +\chapter{Publications} + +Pendant le travail de cette thèse, plusieurs articles ont été produits en explicitant les contributions réalisées, en parallèle d'autres publications ont été produites dans le cadre de la recherche en informatique.\\ + +\section{Publications par rapport au sujet de thèse} + +Daniel Soto Forero; Julien Henriet; Marie-Laure Betbeder. Ensemble Stacking Case-Based Reasoning, Stochastic Recommander Model and Hawkes process Applied to ITS AI-VT. 2025.\\ + +Daniel Soto Forero; Julien Henriet; Marie-Laure Betbeder. Ensemble Stacking Case-Based Reasoning and Stochastic Recommander Model Applied to ITS AI-VT. 2025.\\ + +Daniel Soto Forero; Julien Henriet; Marie-Laure Betbeder. Integration of Stacking Case Based Reasoning with Multi-Agents System Applied to Regression Problems. 2025.\\ + +Daniel Soto Forero; Simha Ackermann; Marie-Laure Betbeder; Julien Henriet. The Intelligent Tutoring System AI-VT with Case-Based Reasoning and Real Time Recommender Models. International Conference on Case Based Reasoning (ICCBR). 2024.\\ + +Daniel Soto Forero; Marie-Laure Betbeder; Julien Henriet. Ensemble Stacking Case-Based Reasoning for Regression. International Conference on Case Based Reasoning (ICCBR). 2024.\\ + +Daniel Soto Forero; Simha Ackermann; Marie-Laure Betbeder; Julien Henriet. Automatic Real-Time Adaptation of Training Session Difficulty Using Rules and Reinforcement Learning in the AI-VT ITS. International Journal of Modern Education and Computer Science (IJMECS). 2024.\\ + +\section{Autres publications} + +Daniel Soto Forero; Yony Ceballos. Metaheuristics Hybridation and Parametrization using Machine Learning. 2025.\\ + +Daniel Soto Forero; Wilson Soto Forero. Efficient Exploration in Unknown Environments: An Adaptative Multi-Agent Approach. 19th Iberian Conference on Information Systems and Technologies. 2024.\\ + +Daniel Soto Forero; Yony Ceballos. Stochastic agent-based models optimization applied to the problem of rebalancing bike-share systems. International Journal of Electrical and Computer Engineering. 2024.\\ + +Daniel Soto Forero; Wilson Soto Forero. A Multi-Agent Based Algorithm for Quadratic Assignment Problem. 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Il est donc nécessaire de trouver des techniques et des algorithmes capables d'exploiter les données disponibles et d'explorer les options d'apprentissage de manière dynamique, afin d'améliorer les performances globales des EIAH. + +Dans ce chapitre seront detaillées les contributions réalisées avec l'incorporation du processus de Hawkes : + +\begin{itemize} + \item Simulation de la courbe d'oubli dans le processus d'apprentissage à l'aide du processus stochastique de Hawkes. + \item Intégration du raisonnement par cas, des systèmes multi-agents et du processus de Hawkes dans un algorithme de recommandation. + \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} + +\section{Modèle Proposé} +L'algorithme proposé est une intégration de la recommandation stochastique (basée 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 basé 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}. + +\begin{figure}[!ht] + \centering + \includegraphics[width=0.5\linewidth]{Figures/Model.png} + \caption{Architecture Proposed Algorithm} + \label{fig:Amodel} +\end{figure} + +La première étape est l'adaptation avec l'échantillonnage de Thompson et la prédiction de l'ECBR-SMA, et enfin la prise de décision pour l'envoi à l'apprenant. Le système de recommandation obtient une valeur de probabilité pour tous les niveaux de complexité pour l'apprenant et l'ECBR-SMA évalue la proposition avec une prédiction pour chaque niveau de complexité. Le tableau \ref{tabvp} présente les variables et les paramètres de l'algorithme proposé et les mesures employées. + +\begin{table}[!ht] + \centering + \begin{tabular}{c|c|c|c} + ID&Type&Description&Domain\\ + \hline + $\alpha$&p&Beta distribution parameter&$[1, \infty] \in \mathbb{R}$\\ + $\beta$&p&Beta distribution parameter&$[1, \infty] \in \mathbb{R}$\\ + $t$&p&Time defined as iterations&$\mathbb{N}$\\ + $c$&p&Complexity level&$\mathbb{N}$\\ + $x_c$&p&Mean grades for complexity level $c$&$\mathbb{R}$\\ + $y_c$&p&Number of questions for complexity level $c$&$\mathbb{N}$\\ + $k_{t,c}$&v&Knowledge evolution in time $t$ for complexity level $c$&$[0,1] \in \mathbb{R}$\\ + $vk_{t,c}$&v&Knowledge evolution for each complexity level $c$&$\mathbb{R}$\\ + $TS_c$&v&Thompson sampling reward for a complexity level $c$&$[0,1] \in \mathbb{R}$\\ + $TSN_c$&v&Normalization of $TS_c$ with others complexity levels&$[0,1] \in \mathbb{R}$\\ + $ESCBR_c$&v&Grade prediction for a complexity level $c$&$\mathbb{R}_+$\\ + $p_c$&f&Probability density function for complexity level $c$&$\mathbb{R}_+$\\ + $D_{JS}$&f&Jensen-Shannon divergence&$[0,1] \in \mathbb{R}$\\ + $r$&f&Recommender metric function&$[0,1] \in \mathbb{R}$\\ + \end{tabular} + \caption{Parameters (p), variables (v) and functions (f) of proposed algorithm and metrics} + \label{tabvp} +\end{table} + +L'intégration se fait en trois étapes. Tout d'abord, sont obtenus les valeurs aléatoires pour chaque niveau de complexité $c$ en utilisant les distributions de probabilité générées avec le TS (équation \ref{IntEq1}), une fois que toutes les valeurs de probabilité correspondant à tous les niveaux de complexité ont été obtenues, la normalisation de toutes ces valeurs est calculée comme indiqué dans l'équation \ref{IntEq2}. Les valeurs de normalisation servent de paramètres de priorité pour les prédictions effectuées par l'ESCBR-SMA, comme le montre l'équation \ref{eqMixModels}. + +\begin{equation} + TS_c=rand(Beta(\alpha_c, \beta_c)) + \label{IntEq1} +\end{equation} + +\begin{equation} + TSN_c=\frac{TS_c}{\sum_{i=0}^4TS_i} + \label{IntEq2} +\end{equation} + +\begin{equation} + n_c=argmax_c(TSN_c*ESCBR_c) + \label{eqMixModels} +\end{equation} + +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}). + +Après la sélection du niveau de complexité, toutes les distributions de probabilité sont mises à jour selon le processus de Hawkes (équation \ref{hp1}) pour chaque paramètre $\alpha$ et $\beta$ en utilisant la fonction d'intensité définie constante (équations \ref{hp21} et \ref{hp22}) et la fonction d'excitation (équation \ref{hp31}). En simulant la courbe d'oubli dans lévolution de la distribution de probabilité Beta. + +\begin{equation} + \lambda(t)=\mu(t)+\sum_{t_i{\centering\arraybackslash}p{8cm}|c} + ID&Type&Description&Domain\\ + \hline + $\alpha$&p&Paramètre de la distribution bêta&$[1, \infty] \in \mathbb{R}$\\ + $\beta$&p&Paramètre de la distribution bêta&$[1, \infty] \in \mathbb{R}$\\ + $t$&p&Temps défini comme itérations&$\mathbb{N}$\\ + $c$&p&Niveau de complexité&$\mathbb{N}$\\ + $k_{t,c}$&v&Évolution de la connaissance dans le temps $t$ pour le niveau de complexité $c$&$[0,1] \in \mathbb{R}$\\ + $vk_{t,c}$&v&Évolution de la connaissance pour chaque niveau de complexité $c$&$\mathbb{R}$\\ + $TS_c$&v&Récompense d'échantillonnage de Thompson pour un niveau de complexité $c$&$[0,1] \in \mathbb{R}$\\ + $TSN_c$&v&Normalization de $TS_c$ avec d'autres niveaux de complexité&$[0,1] \in \mathbb{R}$\\ + $ESCBR_c$&v&Prédiction de la note pour un niveau de complexité $c$&$\mathbb{R}_+$\\ + $p_c$&f&Fonction de densité de probabilité pour le niveau de complexité $c$&$\mathbb{R}_+$\\ + $D_{JS}$&f&Divergence de Jensen-Shannon&$[0,1] \in \mathbb{R}$\\ + + \end{tabular} + \caption{Paramètres (p), variables (v) et fonctions (f) du modèle proposé et les métriques utilisées} + \label{tabvp} +\end{table} + +L'intégration se fait en trois étapes. Tout d'abord, il est nécessaire d'avoir des valeurs aléatoires pour chaque niveau de complexité $c$ en utilisant les distributions de probabilité générées avec le modèle TS (équation \ref{IntEq1}), une fois que toutes les valeurs de probabilité correspondant à tous les niveaux de complexité ont été obtenues, la normalisation de toutes ces valeurs est calculée comme indiqué dans l'équation \ref{IntEq2}. Les valeurs de normalisation servent de paramètres de priorité pour les prédictions effectuées par le modèle ESCBR-SMA, comme le montre l'équation \ref{eqMixModels}. + +\begin{equation} + TS_c=rand(Beta(\alpha_c, \beta_c)) + \label{IntEq1} +\end{equation} + +\begin{equation} + TSN_c=\frac{TS_c}{\sum_{i=0}^4TS_i} + \label{IntEq2} +\end{equation} + +\begin{equation} + n_c=argmax_c(TSN_c*ESCBR_c) + \label{eqMixModels} +\end{equation} + +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} + +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. + +La base de données a été générée avec la distribution logit-normale pour simuler les notes des apprenants, car il s'agit d'un bon modèle pour se rapprocher du monde réel. La base de données représente les notes et les temps de réponse d'un apprenant pour cinq questions à chaque niveau de complexité. + +Le principal inconvénient de ce système de validation « en situation réelle » est la difficulté de la collecte des données. Cette difficulté est accentuée dans les contextes d'apprentissage autorégulé, puisque les apprenants peuvent quitter la plateforme d'apprentissage à tout moment et que les données peuvent être incomplètes \cite{badier:hal-04092828}. + +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} + +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. + +L'algorithme utilise une fonction noyau pour obtenir la meilleure approximation de la solution du nouveau problème, le problème de l'obtention de la meilleure solution est un problème NP, car la formulation est similaire au problème de Fermat-Weber à N dimensions. Le problème de l'obtention de la meilleure solution est un problème NP, car la formulation est similaire au problème de Fermat-Weber à N dimensions \cite{doi:10.1137/23M1592420}. + +La première série de tests est définie sous la forme de différents scénarios, comme le montre le tableau \ref{tab:scenarios}. Dans le scénario 1 (E1), il s'agit de prédire la note d'un apprenant au premier niveau de complexité, après 3 questions. Le scénario 2 (E2) contient les notes de 8 questions et l'objectif est de prédire la note de 9 questions dans le même niveau de complexité. Le scénario 3 (E3) contient les données permettant de prédire le passage à un niveau de complexité supérieur après 4 questions. Le scénario 4 (E4) contient 4 questions et la prédiction de 2 notes dans un niveau de complexité supérieur. + +\begin{table}[!ht] + \centering + \begin{tabular}{ccc} + Scenario&Features&Output Dimension\\ + \hline + E1 & 5 & 1\\ + E2 & 15& 1\\ + E3 & 9 & 1\\ + E4 & 9 & 2\\ + \end{tabular} + \caption{Description des scénarios} + \label{tab:scenarios} +\end{table} + +Le modèle a été comparé à neuf algorithmes bien connus utilisés pour résoudre les problèmes de régression. La liste des algorithmes est présentée dans le tableau \ref{tabAlgs}. + +\begin{table}[!ht] +\footnotesize +\begin{tabular}{ll|ll} +ID&Algorithm&ID&Algorithm\\ +\hline +A1&Linear Regression&A6&Polinomial Regression\\ +A2&K-Nearest Neighbor&A7&Ridge Regression\\ +A3&Decision Tree&A8&Lasso Regression\\ +A4&Random Forest (Ensemble)&A9&Gradient Boosting (Ensemble)\\ +A5&Multi Layer Perceptron&A10&Proposed Ensemble Stacking CBR\\ +\end{tabular} +\caption{Liste des algorithmes évalués } +\label{tabAlgs} +\end{table} + +Les algorithmes ont été évalués à l'aide de trois mesures (Root Mean Squared Error - RMSE, Median Absolute Error - MedAE, Mean Absolute Error - MAE), dont les résultats figurent dans le tableau \ref{tab:results}, où l'on constate que l'algorithme proposé obtient de meilleurs résultats que les autres algorithmes avec lesquels il a été comparé, sauf dans les cas E1(MedAE), E1(MAE), E2(MedAE), E2(MAE), E3 et E4(MedAE) où les meilleurs résultats sont obtenus par l'algorithme A9, mais l'algorithme proposé occupe la deuxième place dans ces cas avec des résultats très proches. Il est possible de conclure que l'intégration de plusieurs algorithmes de recherche et de génération de solutions dans le cadre des paradigmes CBR et Stacking est efficace dans le cas de l'application à la prédiction des notes des apprenants. + +\begin{table}[!ht] + \centering + \footnotesize + \begin{tabular}{c|cccccccccc} + &\multicolumn{10}{c}{\textbf{Algorithme}}\\ + \hline + & A1&A2&A3&A4&A5&A6&A7&A8&A9&A10\\ + \textbf{Scenario (Metrique)}\\ + \hline +E1 (RMSE)&0.625&0.565&0.741&0.56&0.606&0.626&0.626&0.681&0.541&\textbf{0.54}\\ + E1 (MedAE) & 0.387&0.35&0.46&0.338&0.384&0.387&0.387&0.453&\textbf{0.327}&0.347\\ + E1 (MAE) &0.485&0.436&0.572&0.429&0.47&0.485&0.485&0.544&\textbf{0.414}&0.417\\ + \hline + E2 (RMSE)& 0.562&0.588&0.78&0.571&0.61&0.562&0.562&0.622&0.557&\textbf{0.556}\\ + E2 (MedAE)&0.351&0.357&0.464&0.344&0.398&0.351&0.351&0.415&\textbf{0.334}&0.346\\ + E2 (MAE)&0.433&0.448&0.591&0.437&0.478&0.433&0.433&0.495&\textbf{0.422}&0.429\\ + \hline + E3 (RMSE)&0.591&0.59&0.79&0.57&0.632&0.591&0.591&0.644&\textbf{0.555}&0.558\\ + E3 (MedAE)&0.367&0.362&0.474&0.358&0.404&0.367&0.367&0.433&\textbf{0.336}&0.349\\ + E3 (MAE)&0.453&0.45&0.598&0.441&0.49&0.453&0.453&0.512&\textbf{0.427}&0.43\\ + \hline + E4 (RMSE)&0.591&0.589&0.785&0.568&0.613&0.591&0.591&0.644&0.554&\textbf{0.549}\\ + E4 (MedAE)&0.367&0.362&0.465&0.57&0.375&0.367&0.367&0.433&\textbf{0.336}&0.343\\ + E4 (MAE)&0.453&0.45&0.598&0.438&0.466&0.453&0.453&0.512&0.426&\textbf{0.417}\\ + \end{tabular} + \caption{Résultats de la régression pour la base de données des apprenants avec 100 exécutions} + \label{tab:results} +\end{table} + +\subsection{Progression des connaissances} + +Le modèle de recommandation TS est basé 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}). + +%\begin{equation} +\begin{multline} + k_{t,c}=\frac{1}{2} +\int_{0}^{1}p_c(\alpha_t,\beta_t,x) log \left(\frac{p_c(\alpha_t,\beta_t,x)}{m(p_c(\alpha_{t-1},\beta_{t-1},x),p_c(\alpha_t,\beta_t,x))} \right)dx +\\ ++\frac{1}{2} +\int_{0}^{1}p_c(\alpha_{t-1},\beta_{t-1},x) log \left(\frac{p_c(\alpha_{t-1},\beta_{t-1},x)}{m(p_c(\alpha_{t-1},\beta_{t-1},x),p_c(\alpha_t,\beta_t,x))} \right)dx +\label{eqprog1} +\end{multline} +%\end{equation} + +\begin{multline} + m(p(\alpha_{(t-1)},\beta_{(t-1)},x),p(\alpha_{t},\beta_{t},x))=\frac{1}{2} \left( \frac{x^{\alpha_{(t-1)}-1}(1-x)^{\beta_{(t-1)}-1}}{\int_0^1 u^{\alpha_{(t-1)}-1}(1-u^{\beta_{(t-1)}-1})du} \right )\\ + +\frac{1}{2} \left (\frac{x^{\alpha_{t}-1}(1-x)^{\beta_{t}-1}}{\int_0^1 u^{\alpha_{t}-1}(1-u^{\beta_{t}-1})du} \right ) +%\end{equation} +\label{eqprog2} +\end{multline} + +La progression totale des connaissances en $t$ est la somme des différences entre $t$ et $t-1$ pour tous les $c$ niveaux de complexité calculés avec la divergence de Jensen-Shannon (équation \ref{eqTEK}). en utilisant l'évaluation de la progression de la variabilité (équation \ref{eqVarP}). + +\begin{equation} + vk_{t,c}=\begin{cases} + D_{JS}(Beta(\alpha_{t,c},\beta_{t,c}), Beta(\alpha_{t+1,c},\beta_{t+1,c})), & \frac{\alpha_{t,c}}{\alpha_{t,c}+\beta_{t,c}} < \frac{\alpha_{t+1,c}}{\alpha_{t+1,c}+\beta_{t+1,c}}\\ + -D_{JS}(Beta(\alpha_{t,c},\beta_{t,c}), Beta(\alpha_{t+1,c},\beta_{t+1,c})),& Otherwise + \end{cases} + \label{eqVarP} +\end{equation} + +\begin{equation} + k_t=\sum_{c=4}^{c=0 \lor k_t \neq 0} + \begin{cases} + \alpha_{c-1} vk_{t,c-1};&vk_{t,c} > 0\\ + 0;&Otherwise + \end{cases} + \label{eqTEK} +\end{equation} + +\begin{figure} + \centering + \includegraphics[scale=0.5]{Figures/kEvol_TS.jpg} + \caption{Progression des connaissances avec l'échantillonnage de Thompson selon la divergence de Jensen-Shannon} + \label{fig:evolution} +\end{figure} + +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} + +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. + +\begin{figure} + \centering + \includegraphics[scale=0.5]{Figures/GradesEv.jpg} + \caption{Comparaison de l'évolution des notes entre les algorithmes BKT et TS} + \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. + +\begin{figure} + \centering + \includegraphics[scale=0.5]{Figures/LevelsEv.jpg} + \caption{Comparaison de l'évolution des niveaux entre les algorithmes BKT et TS} + \label{fig:EvCL} +\end{figure} + +\subsection{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} + +Pour établir la différence entre le modèle de recommandation TS et le même modèle associé à la prédiction basée 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}. + +\begin{multline} + k_{t,c}=\frac{1}{2} +\int_{0}^{1}p_c(\alpha_{p1,t},\beta_{p1,t},x) +log \left(\frac{p_c(\alpha_{p1,t},\beta_{p1,t},x)}{m(p_c(\alpha_{p1,t},\beta_{p1,t},x),p_c(\alpha_{p2,t},\beta_{p2,t},x))} \right)dx +\\ ++\frac{1}{2} +\int_{0}^{1}p_c(\alpha_{p2,t},\beta_{p2,t},x) log \left(\frac{p_c(\alpha_{p2,t},\beta_{p2,t},x)}{m(p_c(\alpha_{p1,t},\beta_{p1,t},x),p_c(\alpha_{p2,t},\beta_{p2,t},x))} \right)dx +\label{eqjs4} +\end{multline} +%\end{equation} + +\begin{multline} + m(p(\alpha_{p1,t},\beta_{p1,t},x),p(\alpha_{p2,t},\beta_{p2,t},x))=\frac{1}{2} \left( \frac{x^{\alpha_{p1,t}-1}(1-x)^{\beta_{p1,t}-1}}{\int_0^1 u^{\alpha_{p1,t}-1}(1-u^{\beta_{p1,t}-1})du} \right )\\ + +\frac{1}{2} \left (\frac{x^{\alpha_{p2,t}-1}(1-x)^{\beta_{p2,t}-1}}{\int_0^1 u^{\alpha_{p2,t}-1}(1-u^{\beta_{p2,t}-1})du} \right ) + \label{eqjs5} +%\end{equation} +\end{multline} + +La comparaison entre l'évolution des connaissances présente une bifurcation après la septième question, et l'intégration de l'échantillonnage de Thompson et du raisonnement à partir de cas permet d'améliorer l'évolution des connaissances par rapport au seul modèle d'échantillonnage de Thompson (Figure \ref{fig_cmp2}). Pour toutes les questions de la même session, en moyenne, la progression est supérieure par rapport à l'utilisation du seul modèle d'échantillonnage de Thompson comme modèle de recommandation. + +\begin{figure}[!h] + \centering + \includegraphics[scale=0.23]{Figures/TS-ESCBR.png} + \caption{Normalisation de la différence de progression entre l'échantillonnage de Thompson et l'échantillonnage de Thompson avec ESCBR pour 1000 apprenants} + \label{fig_cmp2} +\end{figure} + +\section{Conclusion} + +Ce chapitre présente un modèle intégré entre deux modèles développés précédemment, un système de recommandation basé sur l'algorithme d'échantillonnage de Thompson et un modèle de régression d'ensemble basé 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. 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(pdftex.def) Requested size: 275.4241pt x 219.2151pt. + [65 <./Figures/Stacking1.png> <./Figures/AutomaticS.png>] [66] +<./Figures/Stacking2.png, id=1174, 743.77875pt x 414.54875pt> +File: ./Figures/Stacking2.png Graphic file (type png) + +Package pdftex.def Info: ./Figures/Stacking2.png used on input line 157. +(pdftex.def) Requested size: 297.50623pt x 165.81656pt. + + +LaTeX Warning: Citation `doi:10.1137/23M1592420' on page 67 undefined on input +line 171. + +[67 <./Figures/Stacking2.png>] + +File: Figures/FW.png Graphic file (type png) + +Package pdftex.def Info: Figures/FW.png used on input line 187. +(pdftex.def) Requested size: 213.71576pt x 160.16595pt. + [68 <./Figures/FW.png>] [69] +<./Figures/boxplot.png, id=1210, 1994.45125pt x 959.585pt> +File: ./Figures/boxplot.png Graphic file (type png) + +Package pdftex.def Info: ./Figures/boxplot.png used on input line 292. +(pdftex.def) Requested size: 398.88318pt x 191.91359pt. + [70 <./Figures/boxplot.png (PNG copy)>]) [71] +\openout2 = `./chapters/ESCBR-SMA.aux'. + + (./chapters/ESCBR-SMA.tex [72 + + + + +] +Chapitre 8. + +LaTeX Warning: Citation `KAMALI2023110242' on page 73 undefined on input line 7 +. + + +LaTeX Warning: Citation `DIDDEN2023338' on page 73 undefined on input line 7. -Underfull \hbox (badness 10000) in paragraph at lines 85--86 +LaTeX Warning: Citation `HIPOLITO2023103510' on page 73 undefined on input line + 9. + + +LaTeX Warning: Citation `ZHANG2023110564' on page 73 undefined on input line 9. + + + +LaTeX Warning: Citation `10.1007/978-3-031-63646-2_11' on page 73 undefined on +input line 11. + + +Underfull \vbox (badness 10000) has occurred while \output is active [] + + [73] + +File: Figures/NCBR.png Graphic file (type png) + +Package pdftex.def Info: Figures/NCBR.png used on input line 19. +(pdftex.def) Requested size: 405.15889pt x 289.67882pt. + +Overfull \hbox (182.69249pt too wide) has occurred while \output is active +\T1/phv/m/n/10.95 74 \T1/phv/m/sl/10.95 CHAPITRE 8. INTÉGRATION DU RAISONNEMEN +T À PARTIR DE CAS (RÀPC) ET DES SYSTÈMES MULTI-AGENT (SMA) [] -[65 <./Figures/Stacking1.png> <./Figures/AutomaticS.png>] -Underfull \hbox (badness 10000) in paragraph at lines 97--98 +[74 <./Figures/NCBR.png>] + +File: Figures/FlowCBR.png Graphic file (type png) + +Package pdftex.def Info: Figures/FlowCBR.png used on input line 33. +(pdftex.def) Requested size: 270.41232pt x 493.24655pt. + [75] +Overfull \hbox (182.69249pt too wide) has occurred while \output is active +\T1/phv/m/n/10.95 76 \T1/phv/m/sl/10.95 CHAPITRE 8. INTÉGRATION DU RAISONNEMEN +T À PARTIR DE CAS (RÀPC) ET DES SYSTÈMES MULTI-AGENT (SMA) + [] +[76 <./Figures/FlowCBR.png>] + +File: Figures/agent.png Graphic file (type png) + +Package pdftex.def Info: Figures/agent.png used on input line 99. +(pdftex.def) Requested size: 246.61969pt x 281.7507pt. + [77] + +File: Figures/BayesianEvolution.png Graphic file (type png) + +Package pdftex.def Info: Figures/BayesianEvolution.png used on input line 112. + +(pdftex.def) Requested size: 313.16922pt x 201.25137pt. + +Overfull \hbox (182.69249pt too wide) has occurred while \output is active +\T1/phv/m/n/10.95 78 \T1/phv/m/sl/10.95 CHAPITRE 8. INTÉGRATION DU RAISONNEMEN +T À PARTIR DE CAS (RÀPC) ET DES SYSTÈMES MULTI-AGENT (SMA) [] +[78 <./Figures/agent.png>] [79 <./Figures/BayesianEvolution.png>] +Underfull \hbox (badness 10000) in paragraph at lines 185--185 +[]|\T1/phv/m/n/8 Input. + [] -Underfull \hbox (badness 10000) in paragraph at lines 104--105 +Underfull \hbox (badness 10000) in paragraph at lines 185--186 +[]|\T1/phv/m/n/8 Output [] + +File: Figures/boxplot2.png Graphic file (type png) + +Package pdftex.def Info: Figures/boxplot2.png used on input line 283. +(pdftex.def) Requested size: 419.89888pt x 217.12607pt. -Underfull \hbox (badness 10000) in paragraph at lines 114--115 +Overfull \hbox (182.69249pt too wide) has occurred while \output is active +\T1/phv/m/n/10.95 80 \T1/phv/m/sl/10.95 CHAPITRE 8. INTÉGRATION DU RAISONNEMEN +T À PARTIR DE CAS (RÀPC) ET DES SYSTÈMES MULTI-AGENT (SMA) + [] +[80] [81]) +Overfull \hbox (182.69249pt too wide) has occurred while \output is active +\T1/phv/m/n/10.95 82 \T1/phv/m/sl/10.95 CHAPITRE 8. INTÉGRATION DU RAISONNEMEN +T À PARTIR DE CAS (RÀPC) ET DES SYSTÈMES MULTI-AGENT (SMA) [] +[82 <./Figures/boxplot2.png>] +\openout2 = `./chapters/TS_ESCBR-SMA.aux'. -Underfull \hbox (badness 10000) in paragraph at lines 122--123 + (./chapters/TS_ESCBR-SMA.tex +Chapitre 9. +LaTeX Warning: Citation `jmse11050890' on page 83 undefined on input line 16. + +[83 + + + + +] + +LaTeX Warning: Citation `ZHANG2018189' on page 84 undefined on input line 18. + + +LaTeX Warning: Citation `NEURIPS2023_9d8cf124' on page 84 undefined on input li +ne 35. + + +LaTeX Warning: Citation `pmlr-v238-ou24a' on page 84 undefined on input line 35 +. + + +LaTeX Warning: Citation `math12111758' on page 84 undefined on input line 35. + + +LaTeX Warning: Citation `NGUYEN2024111566' on page 84 undefined on input line 3 +5. + + +Overfull \hbox (282.21376pt too wide) has occurred while \output is active +\T1/phv/m/n/10.95 84 \T1/phv/m/sl/10.95 CHAPITRE 9. 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APPLICATION DU RAISONNEMEN +T À PARTIR DE CAS (RÀPC) ET DES SYSTÈMES MULTI-AGENT (SMA) AU SYSTÈME AI-VT [] +[86] + +File: Figures/Model.png Graphic file (type png) + +Package pdftex.def Info: Figures/Model.png used on input line 147. +(pdftex.def) Requested size: 213.71576pt x 175.76495pt. + [87 <./Figures/Model.png>] + +LaTeX Warning: Citation `badier:hal-04092828' on page 88 undefined on input lin +e 202. -Underfull \hbox (badness 10000) in paragraph at lines 134--135 +Overfull \hbox (282.21376pt too wide) has occurred while \output is active +\T1/phv/m/n/10.95 88 \T1/phv/m/sl/10.95 CHAPITRE 9. 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APPLICATION DU RAISONNEME +NT À PARTIR DE CAS (RÀPC), DES SYSTÈMES MULTI-AGENTS (SMA) ET DU PROCESSUS DE H +AWKES AU SYSTÈME AI-VT [] +[96] [97] + +LaTeX Warning: Citation `Kuzilek2017' on page 98 undefined on input line 124. -Underfull \vbox (badness 2088) has occurred while \output is active [] +<./Figures/stabilityBoxplot1.png, id=1470, 742.775pt x 520.94624pt> +File: ./Figures/stabilityBoxplot1.png Graphic file (type png) + +Package pdftex.def Info: ./Figures/stabilityBoxplot1.png used on input line 12 +8. +(pdftex.def) Requested size: 213.71576pt x 149.88614pt. + +File: Figures/stabilityBoxplot2.png Graphic file (type png) + +Package pdftex.def Info: Figures/stabilityBoxplot2.png used on input line 129. - [67 <./Figures/Stacking2.png>] -Underfull \hbox (badness 10000) in paragraph at lines 173--174 +(pdftex.def) Requested size: 213.71576pt x 149.88614pt. +Overfull \hbox (454.39867pt too wide) has occurred while \output is active +\T1/phv/m/n/10.95 98 \T1/phv/m/sl/10.95 CHAPITRE 10. APPLICATION DU RAISONNEME +NT À PARTIR DE CAS (RÀPC), DES SYSTÈMES MULTI-AGENTS (SMA) ET DU PROCESSUS DE H +AWKES AU SYSTÈME AI-VT [] - -File: Figures/FW.png Graphic file (type png) - -Package pdftex.def Info: Figures/FW.png used on input line 187. -(pdftex.def) Requested size: 213.71576pt x 160.16595pt. -[68 <./Figures/FW.png>] -Underfull \hbox (badness 10000) in paragraph at lines 200--201 +[98] [99 <./Figures/stabilityBoxplot1.png (PNG copy)> <./Figures/stabilityBoxpl +ot2.png (PNG copy)>] + +File: Figures/Var.png Graphic file (type png) + +Package pdftex.def Info: Figures/Var.png used on input line 165. +(pdftex.def) Requested size: 427.43153pt x 227.57355pt. + +File: Figures/VarH.png Graphic file (type png) + +Package pdftex.def Info: Figures/VarH.png used on input line 171. +(pdftex.def) Requested size: 427.43153pt x 227.57355pt. + +Underfull \vbox (badness 10000) has occurred while \output is active [] + +Overfull \hbox (460.48679pt too wide) has occurred while \output is active +\T1/phv/m/n/10.95 100 \T1/phv/m/sl/10.95 CHAPITRE 10. APPLICATION DU RAISONNEM +ENT À PARTIR DE CAS (RÀPC), DES SYSTÈMES MULTI-AGENTS (SMA) ET DU PROCESSUS DE +HAWKES AU SYSTÈME AI-VT [] +[100 <./Figures/Var.png> <./Figures/VarH.png>]) [101] +\openout2 = `./chapters/Conclusions.aux'. + + +(./chapters/Conclusions.tex [102 + + + + +] +Chapitre 11. -Underfull \hbox (badness 10000) in paragraph at lines 223--224 +Underfull \hbox (badness 10000) in paragraph at lines 4--5 [] +[103]) [104] +\openout2 = `./chapters/Publications.aux'. -Underfull \hbox (badness 10000) in paragraph at lines 241--242 + (./chapters/Publications.tex +Chapitre 12. + +Underfull \hbox (badness 10000) in paragraph at lines 3--4 [] -<./Figures/boxplot.png, id=1021, 1994.45125pt x 959.585pt> -File: ./Figures/boxplot.png Graphic file (type png) - -Package pdftex.def Info: ./Figures/boxplot.png used on input line 292. -(pdftex.def) Requested size: 398.88318pt x 191.91359pt. -[69] -Underfull \hbox (badness 10000) in paragraph at lines 299--300 + +Underfull \hbox (badness 10000) in paragraph at lines 7--8 [] -Underfull \hbox (badness 10000) in paragraph at lines 301--302 +Underfull \hbox (badness 10000) in paragraph at lines 9--10 [] -[70] -Underfull \hbox (badness 10000) in paragraph at lines 303--304 + +Underfull \hbox (badness 10000) in paragraph at lines 11--12 [] -Underfull \hbox (badness 10000) in paragraph at lines 305--306 +Underfull \hbox (badness 10000) in paragraph at lines 13--14 + + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 15--16 + + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 17--18 + + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 21--22 + + [] + + +Underfull \vbox (badness 10000) has occurred while \output is active [] + + [105 + + + + +] +Underfull \hbox (badness 10000) in paragraph at lines 23--24 + + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 25--26 [] ) -Underfull \hbox (badness 10000) in paragraph at lines 311--374 +Underfull \hbox (badness 10000) in paragraph at lines 27--384 [] -[71 <./Figures/boxplot.png (PNG copy)>] [72] (./main.bbl +[106] (./main.bbl Underfull \hbox (badness 1394) in paragraph at lines 79--85 []\T1/phv/m/n/10.95 Henriet, J., Chris-tophe, L., and Laurent, P. (2017). Ar-t i-fi-cial [] -[73 +[107 @@ -1861,32 +2203,34 @@ Underfull \hbox (badness 1939) in paragraph at lines 179--183 []\T1/phv/m/n/10.95 Muangprathub, J., Boon-jing, V., and Cham-nong-thai, K. [] -[74] +[108] Underfull \hbox (badness 2452) in paragraph at lines 216--220 []\T1/phv/m/n/10.95 Petrovic, S., Khus-sai-nova, G., and Ja-gan-na-than, R. (20 16). [] -[75] [76]) [77] [78 +[109] [110]) [111] [112 ] -LaTeX Font Info: Trying to load font information for T1+pcr on input line 38 -6. +LaTeX Font Info: Trying to load font information for T1+pcr on input line 39 +2. (/usr/local/texlive/2023/texmf-dist/tex/latex/psnfss/t1pcr.fd File: t1pcr.fd 2001/06/04 font definitions for T1/pcr. -) [79] - +) [113] + File: spimufcphdthesis-backpage.pdf Graphic file (type pdf) -Package pdftex.def Info: spimufcphdthesis-backpage.pdf used on input line 386. +Package pdftex.def Info: spimufcphdthesis-backpage.pdf used on input line 392. 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