From 7f254e8923b0c38030d8f55b625c9bcc8fd54173 Mon Sep 17 00:00:00 2001 From: Quarto GHA Workflow Runner Date: Wed, 27 Nov 2024 13:32:26 +0000 Subject: [PATCH] Built site for gh-pages --- .nojekyll | 2 +- chapters/chapter2/3-random_forest.html | 6 ++--- chapters/chapter3/2-guide_usage_RF.html | 34 +++++++++++------------- pdf/dt_methodes_ensemblistes.pdf | Bin 900080 -> 899653 bytes pdf/partie_toute_redigee.pdf | Bin 719266 -> 718823 bytes search.json | 8 +++--- sitemap.xml | 22 +++++++-------- 7 files changed, 34 insertions(+), 38 deletions(-) diff --git a/.nojekyll b/.nojekyll index 1ed2294..9f45aed 100644 --- a/.nojekyll +++ b/.nojekyll @@ -1 +1 @@ -f815bd2f \ No newline at end of file +a120803e \ No newline at end of file diff --git a/chapters/chapter2/3-random_forest.html b/chapters/chapter2/3-random_forest.html index 219c33c..eadb78a 100644 --- a/chapters/chapter2/3-random_forest.html +++ b/chapters/chapter2/3-random_forest.html @@ -263,7 +263,7 @@

On this page

  • Evaluation des performances par l’erreur Out-of-Bag (OOB)
  • Interprétation et importance des variables @@ -415,8 +415,8 @@

    Louppe (2014)). Plusieurs travaux théoriques ont toutefois fourni des preuves de convergence pour des versions simplifiées de l’algorithme (par exemple, Biau (2012)).

    Par ailleurs, une propriété importante des forêts aléatoires démontrée par Breiman (2001) est que leur erreur de généralisation, c’est-à-dire l’écart entre les prédictions du modèle et les résultats attendus sur des données jamais vues (donc hors de l’échantillon d’entraînement), diminue à mesure que le nombre d’arbres augmente et converge vers une valeur constante. Autrement dit, la forêt aléatoire ne souffre pas d’un surapprentissage croissant avec le nombre d’arbres. La conséquence pratique de ce résultat est qu’inclure un (trop) grand nombre d’arbres dans le modèle n’en dégrade pas la qualité, ce qui contribue à la rendre particulièrement robuste. En revanche, une forêt aléatoire peut souffrir de surapprentissage si ses autres hyperparamètres sont mal choisis (des arbres trop profonds par exemple).

    -
    -

    Facteurs influençant l’erreur de généralisation

    +
    +

    Facteurs influençant l’erreur de généralisation

    L’erreur de généralisation des forêts aléatoires est influencée par deux facteurs principaux :

    • La puissance prédictrice des arbres individuels : Les arbres doivent être suffisamment prédictifs pour contribuer positivement à l’ensemble, et idéalement sans biais.

    • diff --git a/chapters/chapter3/2-guide_usage_RF.html b/chapters/chapter3/2-guide_usage_RF.html index 9972bd3..3d2411b 100644 --- a/chapters/chapter3/2-guide_usage_RF.html +++ b/chapters/chapter3/2-guide_usage_RF.html @@ -260,7 +260,7 @@

      On this page

    • Les hyperparamètres clés des forêts aléatoires
    • Comment entraîner une forêt aléatoire?
    • Mesurer l’importance des variables
    • @@ -276,14 +276,14 @@

      On this page

      Guide d’entraînement des forêts aléatoires

      -

      Ce guide d’entraînement des forêts aléatoires rassemble et synthétise des recommandations sur l’entraînement des forêts aléatoires disponibles dans la littérature, en particulier dans Probst, Wright, and Boulesteix (2019). Ce guide comporte un certain nombre de choix méthodologiques forts, comme les implémentations recommandées ou la procédure d’entraînement proposée, et d’autres choix sont évidemment possibles. Les recommandations de ce guide doivent donc être considérées comme un point de départ raisonnable, pas comme un ensemble de règles devant être respectées à tout prix.

      +

      Ce guide d’entraînement des forêts aléatoires rassemble et synthétise des recommandations sur l’entraînement des forêts aléatoires disponibles dans la littérature, en particulier dans Probst, Wright, and Boulesteix (2019). Ce guide comporte un certain nombre de choix méthodologiques forts, comme les implémentations recommandées ou la procédure d’entraînement proposée, et d’autres choix pertinents sont évidemment possibles. C’est pourquoi les recommandations de ce guide doivent être considérées comme un point de départ raisonnable, pas comme un ensemble de règles devant être respectées à tout prix.

      Quelles implémentations utiliser?

      Il existe de multiples implémentations des forêts aléatoires. Le présent document présente et recommande l’usage de deux implémentations de référence: le package R ranger et le package Python scikit-learn pour leur rigueur, leur efficacité et leur simplicité d’utilisation. Il est à noter qu’il est possible d’entraîner des forêts aléatoires avec les algorithmes XGBoost et LightGBM, mais il s’agit d’un usage avancé qui n’est pas recommandé en première approche. Cette approche est présentée dans la partie REFERENCE A LA PARTIE USAGE AVANCE.

      Les hyperparamètres clés des forêts aléatoires

      -

      Cette section décrit en détail les principaux hyperparamètres des forêts aléatoires listés dans le tableau . Les noms des hyperparamètres utilisés sont ceux figurant dans le package R ranger, et dans le package Python scikit-learn. Il arrive qu’ils portent un nom différent dans d’autres implémentations des random forests, mais il est généralement facile de s’y retrouver en lisant attentivement la documentation.

      +

      Cette section décrit en détail les principaux hyperparamètres des forêts aléatoires listés dans le tableau . Les noms des hyperparamètres utilisés sont ceux figurant dans le package R ranger, et dans le package Python scikit-learn. Il arrive qu’ils portent un nom différent dans d’autres implémentations des forêts aléatoires, mais il est généralement facile de s’y retrouver en lisant attentivement la documentation.

      @@ -333,11 +333,7 @@

      Les hyperparamètres cl

      Les principaux hyperparamètres des forêts aléatoires
      • Le nombre d’arbres par défaut varie selon les implémentations (500 dans ranger, 100 dans scikit-learn). Il s’agit d’un hyperparamètre particulier car il n’est associé à aucun arbitrage en matière de performance: la performance de la forêt aléatoire croît avec le nombre d’arbres, puis se stabilise. Le nombre optimal d’arbres est celui à partir duquel la performance de la forêt ne croît plus (ce point est détaillé plus bas) où à partir duquel l’ajout d’arbres supplémentaires génère des gains marginaux. Il est important de noter que ce nombre optimal dépend des autres hyperparamètres. Par exemple, un taux d’échantillonnage faible et un nombre faible de variables candidates à chaque noeud aboutissent à des arbres peu corrélés, mais peu performants, ce qui requiert probablement un plus grand nombre d’arbres. L’utilisation de mesures comme le score de Brier est recommandée pour évaluer la convergence plutôt que le taux d’erreur.

      • -
      • Le nombre (ou la part) de variables candidates à chaque noeud (souvent appelé mtry) est un hyperparamètre fondamental qui détermine le nombre de variables prédictives sélectionnées aléatoirement à chaque nœud lors de la construction des arbres. Ce paramètre exerce la plus forte influence sur les performances du modèle.

      • -
      -

      Un nombre plus faible de variables candidates conduit à des arbres moins performants mais plus diversifiés et donc moins corrélés entre eux. À l’inverse, un nombre plus élevé de variables candidates améliore la précision des arbres individuels mais accroît leur corrélation (les mêmes variables ayant tendance à être sélectionnées dans tous les arbres), limitant ainsi les bénéfices de l’agrégation en termes de réduction de variance. Un compromis doit être trouvé et le choix optimal dépend du nombre de variables réellement pertinentes dans les données. Une faible valeur de mtry est préférable lorsque la plupart des variables sont pertinentes, tandis qu’une valeur élevé est meilleure lorsqu’il y a peu de variables pertinentes parmi l’ensemble des variables considérées. Par ailleurs, une valeur élevée de mtry est préférable si les données comprennent un grand nombre de variables binaires issues du one-hot-encoding des variables catégorielles (LIEN AVEC LA PARTIE PREPROCESSING).

      -

      Par défaut, cette valeur est fréquemment fixée à \(\sqrt{p}\) pour les problèmes de classification et à \(p/3\) pour les problèmes de régression, où \(p\) représente le nombre total de variables prédictives disponibles. Ces choix par défaut reposent sur des heuristiques empiriques qui offrent généralement un bon compromis entre la précision des prédictions et la diversité des arbres.

      -
        +
      • Le nombre (ou la part) de variables candidates à chaque noeud (souvent appelé mtry) est un hyperparamètre essentiel qui détermine le nombre de variables prédictives sélectionnées aléatoirement à chaque nœud lors de la construction des arbres. Ce paramètre exerce la plus forte influence sur les performances du modèle, et un compromis doit être trouvé entre puissance prédictive des arbres et corrélation entre arbres. Une faible valeur de mtry conduit à des arbres moins performants mais plus diversifiés et donc moins corrélés entre eux. Inversement, une valeur plus élevée améliore la précision des arbres individuels mais accroît leur corrélation (les mêmes variables ayant tendance à être sélectionnées dans tous les arbres). La valeur optimale de mtry dépend du nombre de variables réellement pertinentes dans les données: elle est plus faible lorsque la plupart des variables sont pertinentes, et plus élevée lorsqu’il y a peu de variables pertinentes. Par ailleurs, une valeur élevée de mtry est préférable si les données comprennent un grand nombre de variables binaires issues du one-hot-encoding des variables catégorielles (LIEN AVEC LA PARTIE PREPROCESSING). Par défaut, cette valeur est fréquemment fixée à \(\sqrt{p}\) pour les problèmes de classification et à \(p/3\) pour les problèmes de régression, où \(p\) représente le nombre total de variables prédictives disponibles.

      • Le taux d’échantillonnage et le mode de tirage contrôlent le plan d’échantillonnage des données d’entraînement. Les valeurs par défaut varient d’une implémentation à l’autre; dans le cas de ranger, le taux d’échantillonnage est de 63,2% sans remise, et de 100% avec remise. L’implémentation scikit-learn ne propose pas le tirage sans remise. Ces hyperparamètres ont des effets sur la performance similaires à ceux du nombre de variables candidates, mais d’une moindre ampleur. Un taux d’échantillonnage plus faible aboutit à des arbres plus diversifiés et donc moins corrélés (car ils sont entraînés sur des échantillons très différents), mais ces arbres peuvent être peu performants car ils sont entraînés sur des échantillons de petite taille. Inversement, un taux d’échantillonnage élevé aboutit à des arbres plus performants mais plus corrélés. Les effets de l’échantillonnage avec ou sans remise sur la performance de la forêt aléatoire sont moins clairs et ne font pas consensus. Les travaux les plus récents semblent toutefois suggérer qu’il est préférable d’échantillonner sans remise (Probst, Wright, and Boulesteix (2019)).

      • Le nombre minimal d’observations dans les noeuds terminaux contrôle la taille des noeuds terminaux. La valeur par défaut est faible dans la plupart des implémentations (entre 1 et 5). Il n’y a pas vraiment de consensus sur l’effet de cet hyperparamètre sur les performances, bien qu’une valeur plus faible augmente le risque de sur-apprentissage. En revanche, il est certain que le temps d’entraînement décroît fortement avec cet hyperparamètre: une valeur faible implique des arbres très profonds, avec un grand nombre de noeuds. Il peut donc être utile de fixer ce nombre à une valeur plus élevée pour accélérer l’entraînement, en particulier si les données sont volumineuses et si on utilise une méthode de validation croisée pour le choix des autres hyperparamètres. Cela se fait généralement sans perte significative de performance.

      • Le critère de choix de la règle de division des noeuds intermédiaires: la plupart des implémentations des forêts aléatoires retiennent par défaut l’impureté de Gini pour la classification et la variance pour la régression, même si d’autres critères de choix ont été proposés dans la littérature (p-value dans les forêts d’inférence conditionnelle, arbres extrêmement randomisés, etc.). Chaque règle présente des avantages et des inconvénients, notamment en termes de biais de sélection des variables et de vitesse de calcul. A ce stade, aucun critère de choix ne paraît systématiquement supérieur aux autres en matière de performance. Modifier cet hyperparamètre relève d’un usage avancé des forêts aléatoires. Le lecteur intéressé pourra se référer à la discussion détaillée dans Probst, Wright, and Boulesteix (2019).

      • @@ -346,17 +342,17 @@

        Les hyperparamètres cl

        Comment entraîner une forêt aléatoire?

        Les forêts aléatoires nécessitent généralement moins d’optimisation que d’autres modèles de machine learning, car leurs performances varient relativement peu en fonction des hyperparamètres. Les valeurs par défaut fournissent souvent des résultats satisfaisants, ce qui réduit le besoin d’optimisation intensive. Cependant, un ajustement précis des hyperparamètres peut apporter des gains de performance, notamment sur des jeux de données complexes.

        -

        Comme indiqué dans la partie REFERENCE A AJOUTER, la performance prédictive d’une forêt aléatoire varie en fonction de deux critères essentiels: elle croît avec le pouvoir prédictif des arbres, et décroît avec la corrélation des arbres entre eux. L’entraînement d’une forêt aléatoire implique de trouver un équilibre optimal où les arbres sont suffisamment puissants pour être prédictifs, tout en étant suffisamment diversifiés pour que leurs erreurs ne soient pas trop corrélées. Cet arbitrage s’opère en ajustant certains hyperparamètres clés comme le nombre de variables candidates à chaque division, la taille de l’échantillon ou encore la taille minimale des feuilles. L’ajustement du nombre d’arbre relève plutôt d’un arbitrage entre performance et temps de calcul. Il est recommandé de fixer le nombre d’arbre à une valeur au-delà de laquelle les gains de performance peuvent être considérés comme marginaux.

        -

        Il existe plusieurs méthodes permettant d’optimiser simultanément plusieurs hyperparamètres: la recherche par grille, la recherche aléatoire et l’optimisation basée sur modèle séquentiel (SMBO).

        -
        -

        Première approche exploratoire

        +

        Comme indiqué dans la partie ?@sec-facteur-perf-rf, la performance prédictive d’une forêt aléatoire varie en fonction de deux critères essentiels: elle croît avec le pouvoir prédictif des arbres, et décroît avec la corrélation des arbres entre eux. L’optimisation des hyperparamètres d’une forêt aléatoire vise donc à trouver un équilibre optimal où les arbres sont suffisamment puissants pour être prédictifs, tout en étant suffisamment diversifiés pour que leurs erreurs ne soient pas trop corrélées.

        +

        La littérature propose de multiples approches pour optimiser simultanément plusieurs hyperparamètres: la recherche par grille (grid search), la recherche aléatoire (random search) et l’optimisation basée sur modèle séquentiel (SMBO), et il peut être difficile de savoir quelle approche adopter. Ce guide propose donc une première approche délibérément simple, avant de présenter les approches plus avancées.

        +
        +

        Approche simple

        Voici une procédure simple pour entraîner une forêt aléatoire. Elle ne garantit pas l’obtention d’un modèle optimal, mais elle est lisible et permet d’obtenir rapidement un modèle raisonnablement performant.

        • Commencer par entraîner une forêt aléatoire avec les valeurs des hyperparamètres par défaut. Ce premier modèle servira de point de comparaison pour la suite.
        • -
        • Ajuster le nombre d’arbres: entraîner une forêt aléatoire avec les hyperparamètres par défaut en augmentant progressivement le nombre d’arbres, puis déterminer à partir de quel nombre d’arbres la performance se stabilise. Fixer le nombre d’arbres à cette valeur par la suite.
        • -
        • Ajuster le nombre minimal d’observations dans les noeuds terminaux: optimiser cet hyperparamètre grâce à une méthode de grid search évaluée par une approche de validation-croisée. Ce n’est pas l’hyperparamètre le plus important, mais il est utile de vérifier s’il est possible de le fixer à une valeur plus élevée que la valeur par défaut sans perte de performance, car cela permet d’accélérer le reste de la procédure.
        • -
        • Ajuster le nombre de variables candidates et le taux d’échantillonnage: optimiser ces deux hyperparamètres grâce à une méthode de grid search évaluée par une approche de validation-croisée.
        • -
        • Evaluation du modèle final: mesurer la performance du modèle final soit avec l’approche Out-of-Bag (OOB), soit avec un ensemble de test. Il est souvent instructif de comparer les performances du modèle final et du modèle entraîné avec les valeurs des hyperparamètres par défaut.
        • +
        • Ajuster le nombre d’arbres: entraîner une forêt aléatoire avec les hyperparamètres par défaut en augmentant progressivement le nombre d’arbres, puis déterminer à partir de quel nombre d’arbres la performance se stabilise (en mesurant la performance avec l’erreur OOB ou avec le score de Brier). Fixer le nombre d’arbres à cette valeur par la suite.
        • +
        • Ajuster le nombre minimal d’observations dans les noeuds terminaux: optimiser cet hyperparamètre grâce à une méthode de grid search évaluée par une approche de validation-croisée, ou par une approche reposant sur l’erreur OOB. Ce n’est pas l’hyperparamètre le plus important, mais il est utile de vérifier s’il est possible de le fixer à une valeur plus élevée que la valeur par défaut sans perte de performance, car cela permet d’accélérer le reste de la procédure.
        • +
        • Ajuster le nombre de variables candidates et le taux d’échantillonnage: optimiser ces deux hyperparamètres grâce à une méthode de grid search évaluée par une approche de validation-croisée, ou par une approche reposant sur l’erreur OOB.
        • +
        • Evaluation du modèle final: mesurer la performance du modèle final soit avec l’approche Out-of-Bag (OOB), soit avec un ensemble de test. Il est souvent instructif de comparer les performances du modèle final et du modèle entraîné avec les valeurs des hyperparamètres par défaut (parfois pour se rendre compte que ce dernier était déjà suffisamment performant…).
        @@ -376,9 +372,9 @@

        Mesurer

        En pratique, il est recommandé d’utiliser des méthodes d’importance des variables moins sensibles aux biais, comme les CIF ou la Sobol-MDA. Les valeurs de Shapley, issues de la théorie des jeux, sont également une alternative intéressante. Elles attribuent à chaque variable une contribution proportionnelle à son impact sur la prédiction. Cependant, leur calcul est souvent complexe et coûteux en ressources computationnelles, surtout en présence de nombreuses variables. Des méthodes comme SHAFF (SHApley eFfects via random Forests) ont été développées pour estimer efficacement ces valeurs, même en présence de dépendances entre variables.

        On conseille l’utilisation de trois implémentations pour comparer l’importances des variables d’une forêt aléatoire:

          -
        • Pour la MDI: l’algorithme CIF proposé par Strobl et al. (2007) et implémenté en R

        • -
        • Pour la MDA: l’algorithme Sobol-MDA proposé par Bénard, Da Veiga, and Scornet (2022) et implémenté en R

        • -
        • Pour les valeurs de shapley : l’alogrithme SHAFF proposé par Bénard et al. (2022) et implémenté en R

        • +
        • Pour la MDI: l’algorithme CIF proposé par Strobl et al. (2007) et implémenté en R

        • +
        • Pour la MDA: l’algorithme Sobol-MDA proposé par Bénard, Da Veiga, and Scornet (2022) et implémenté en R

        • +
        • Pour les valeurs de Shapley : l’alogrithme SHAFF proposé par Bénard et al. (2022) et implémenté en R

        Enfin, nous recommandons de combiner plusieurs méthodes pour une analyse plus robuste et de tenir compte des prétraitements des données afin de minimiser les biais potentiels.

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