{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Construire un classificateur par arbre de décision\n", "\n", "CSI 4506 — Introduction à l’intelligence artificielle\n", "\n", "Marcel Turcotte \n", "2026-09-15\n", "\n", "# Introduction\n", "\n", "Ce cahier construit un petit classificateur par arbre de décision à\n", "partir des principes fondamentaux. L’objectif n’est pas de concurrencer\n", "scikit-learn, mais de rendre visibles les opérations centrales de\n", "l’algorithme d’apprentissage :\n", "\n", "1. mesurer à quel point les classes d’un nœud sont mélangées;\n", "2. évaluer les divisions candidates;\n", "3. conserver la meilleure division;\n", "4. répéter le processus récursivement.\n", "\n", "L’implémentation accepte des attributs numériques, des divisions\n", "binaires par seuil, plusieurs classes, des prédictions de probabilités\n", "et quelques conditions d’arrêt. Elle omet volontairement les valeurs\n", "manquantes, les attributs catégoriels, les poids d’exemples, la\n", "recherche optimisée des divisions et l’élagage.\n", "\n", "# Préparation\n", "\n", "La seule dépendance non standard est `palmerpenguins`. L’installation ne\n", "s’exécute que si ce paquet est absent, ce qui permet d’utiliser le\n", "cahier dans une nouvelle session Google Colab." ], "id": "501a7a0e-7612-4651-9bca-266d76c4388e" }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import subprocess\n", "import sys\n", "from dataclasses import dataclass\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "try:\n", " from palmerpenguins import load_penguins\n", "except ImportError:\n", " subprocess.check_call([\n", " sys.executable, \"-m\", \"pip\", \"install\", \"-q\", \"palmerpenguins\"\n", " ])\n", " from palmerpenguins import load_penguins\n", "\n", "from sklearn.model_selection import train_test_split" ], "id": "imports" }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Manchots de Palmer\n", "\n", "Nous conservons deux attributs numériques et formulons une tâche de\n", "classification binaire : **Gentoo** ou **pas Gentoo**. Avec seulement\n", "deux attributs, nous pouvons représenter les régions de décision\n", "apprises." ], "id": "1455a163-f699-461b-92e0-dcff5ac24fba" }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Exemples d'entraînement : 273\n", "Exemples de test : 69" ] } ], "source": [ "feature_names = [\"bill_depth_mm\", \"body_mass_g\"]\n", "\n", "penguins = load_penguins()\n", "penguins = penguins[feature_names + [\"species\"]].dropna().copy()\n", "\n", "X = penguins[feature_names].to_numpy()\n", "y = np.where(\n", " penguins[\"species\"].to_numpy() == \"Gentoo\",\n", " \"Gentoo\",\n", " \"Pas Gentoo\",\n", ")\n", "\n", "X_train, X_test, y_train, y_test = train_test_split(\n", " X, y, test_size=0.2, random_state=42, stratify=y\n", ")\n", "\n", "print(f\"Exemples d'entraînement : {len(X_train)}\")\n", "print(f\"Exemples de test : {len(X_test)}\")" ], "id": "penguins-data" }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Entropie\n", "\n", "Pour un nœud dont les proportions des classes sont $p_1,\\ldots,p_K$,\n", "l’entropie est\n", "\n", "$$\n", "H=-\\sum_{k=1}^{K}p_k\\log_2p_k.\n", "$$\n", "\n", "Un nœud pur a une entropie nulle. L’entropie augmente lorsque les\n", "proportions des classes deviennent plus équilibrées." ], "id": "10a2bf03-2acf-46e2-ae83-f9f79936f820" }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def class_probabilities(y, classes):\n", " \"\"\"Retourner la proportion d'exemples de chaque classe.\"\"\"\n", " return np.array([np.mean(y == label) for label in classes])\n", "\n", "\n", "def entropy(y, classes):\n", " \"\"\"Mesurer le mélange des classes; zéro correspond à un nœud pur.\"\"\"\n", " probabilities = class_probabilities(y, classes)\n", " probabilities = probabilities[probabilities > 0]\n", " if len(probabilities) == 1:\n", " return 0.0\n", " return float(-np.sum(probabilities * np.log2(probabilities)))" ], "id": "entropy" }, { "cell_type": "markdown", "metadata": {}, "source": [ "Cette petite vérification retrouve les valeurs binaires familières : un\n", "nœud équilibré possède un bit d’entropie, tandis qu’un nœud pur n’en\n", "possède aucun." ], "id": "f7f8b2f8-f412-4dc9-a3d6-d5d3745c233d" }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Nœud équilibré : 1.000 bit\n", "Nœud pur : 0.000 bit" ] } ], "source": [ "binary_classes = np.array([\"Gentoo\", \"Pas Gentoo\"])\n", "\n", "balanced = np.array([\"Gentoo\", \"Pas Gentoo\"])\n", "pure = np.array([\"Gentoo\", \"Gentoo\"])\n", "\n", "print(f\"Nœud équilibré : {entropy(balanced, binary_classes):.3f} bit\")\n", "print(f\"Nœud pur : {entropy(pure, binary_classes):.3f} bit\")" ], "id": "entropy-check" }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Évaluation d’une division\n", "\n", "Une division candidate crée un enfant gauche et un enfant droit. Nous\n", "l’évaluons au moyen de leur entropie pondérée :\n", "\n", "$$\n", "J=\n", "\\frac{N_{\\mathrm{left}}}{N_{\\mathrm{parent}}}H_{\\mathrm{left}}\n", "+\n", "\\frac{N_{\\mathrm{right}}}{N_{\\mathrm{parent}}}H_{\\mathrm{right}}.\n", "$$\n", "\n", "La pondération empêche un minuscule enfant pur d’avoir autant\n", "d’influence qu’un enfant beaucoup plus grand dont les classes sont\n", "mélangées." ], "id": "9a9e7c54-8b93-49a4-aa2e-13b8152edb43" }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def weighted_entropy(y_left, y_right, classes):\n", " \"\"\"Retourner l'entropie pondérée produite par une division.\"\"\"\n", " n_left = len(y_left)\n", " n_right = len(y_right)\n", " n_parent = n_left + n_right\n", "\n", " return (\n", " n_left / n_parent * entropy(y_left, classes)\n", " + n_right / n_parent * entropy(y_right, classes)\n", " )\n", "\n", "\n", "def candidate_thresholds(values):\n", " \"\"\"Retourner les milieux entre les valeurs distinctes consécutives.\"\"\"\n", " values = np.unique(values)\n", " return (values[:-1] + values[1:]) / 2" ], "id": "split-score" }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Trois divisions candidates\n", "\n", "L’exemple suivant compare les cas présentés en classe. Sans pondération,\n", "isoler un seul exemple pur semble artificiellement avantageux." ], "id": "a99bc4e3-4dd5-47e5-8bbf-dd5d4231cade" }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "désordonnée : non pondérée=0.971, pondérée=0.971\n", " isole un : non pondérée=0.496, pondérée=0.892\n", " utile : non pondérée=0.722, pondérée=0.722" ] } ], "source": [ "split_examples = {\n", " \"désordonnée\": (\n", " np.array([\"Gentoo\"] * 3 + [\"Pas Gentoo\"] * 2),\n", " np.array([\"Gentoo\"] * 2 + [\"Pas Gentoo\"] * 3),\n", " ),\n", " \"isole un\": (\n", " np.array([\"Gentoo\"]),\n", " np.array([\"Gentoo\"] * 4 + [\"Pas Gentoo\"] * 5),\n", " ),\n", " \"utile\": (\n", " np.array([\"Gentoo\"] * 4 + [\"Pas Gentoo\"]),\n", " np.array([\"Gentoo\"] + [\"Pas Gentoo\"] * 4),\n", " ),\n", "}\n", "\n", "for name, (left, right) in split_examples.items():\n", " unweighted = (\n", " entropy(left, binary_classes) + entropy(right, binary_classes)\n", " ) / 2\n", " weighted = weighted_entropy(left, right, binary_classes)\n", " print(f\"{name:>11} : non pondérée={unweighted:.3f}, pondérée={weighted:.3f}\")" ], "id": "split-score-check" }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Recherche gloutonne d’une division\n", "\n", "Pour chaque attribut, nous examinons les milieux entre les valeurs\n", "distinctes consécutives. La fonction conserve la division candidate dont\n", "l’entropie pondérée est la plus faible." ], "id": "1859a8d2-570b-48b3-82c4-7b6edc4e8a33" }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def find_best_split(X, y, classes, min_samples_leaf):\n", " \"\"\"Retourner la meilleure division et le nombre de candidates évaluées.\"\"\"\n", " best_split = None\n", " best_score = entropy(y, classes)\n", " n_candidates = 0\n", "\n", " for feature in range(X.shape[1]):\n", " for threshold in candidate_thresholds(X[:, feature]):\n", " go_left = X[:, feature] <= threshold\n", " n_left = np.sum(go_left)\n", " n_right = len(y) - n_left\n", "\n", " if min(n_left, n_right) < min_samples_leaf:\n", " continue\n", "\n", " n_candidates += 1\n", " score = weighted_entropy(y[go_left], y[~go_left], classes)\n", " if score < best_score:\n", " best_score = score\n", " best_split = (feature, float(threshold), go_left)\n", "\n", " return best_split, n_candidates" ], "id": "best-split" }, { "cell_type": "markdown", "metadata": {}, "source": [ "Cette recherche est gloutonne : elle choisit la meilleure division\n", "immédiate sans réexaminer les décisions précédentes. Elle ne garantit\n", "donc pas de construire l’arbre le plus petit ni un arbre globalement\n", "optimal.\n", "\n", "# Représentation de l’arbre\n", "\n", "Chaque nœud conserve les proportions des classes parmi les exemples qui\n", "l’atteignent. Une feuille utilise ces proportions pour effectuer des\n", "prédictions. Un nœud interne conserve en plus un attribut, un seuil et\n", "deux enfants." ], "id": "c655c1b9-6dd6-46be-aeba-6d373cce514d" }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "@dataclass\n", "class Node:\n", " probabilities: np.ndarray\n", " n_samples: int\n", " loss: float\n", " feature: int | None = None\n", " threshold: float | None = None\n", " left: \"Node | None\" = None\n", " right: \"Node | None\" = None\n", "\n", " @property\n", " def is_leaf(self):\n", " return self.feature is None" ], "id": "node" }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Classificateur\n", "\n", "La méthode récursive `_grow_tree` est au cœur de l’apprentissage. Elle\n", "crée un nœud, vérifie les conditions d’arrêt, trouve une division, puis\n", "construit récursivement ses enfants.\n", "\n", "Les méthodes de validation et de mise en forme du texte facilitent\n", "l’utilisation du classificateur. Il s’agit de code auxiliaire et non de\n", "nouveaux concepts d’apprentissage automatique." ], "id": "5442c2e4-2802-43f2-863d-20fcca32fbb1" }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "class SimpleDecisionTreeClassifier:\n", " \"\"\"Un classificateur didactique avec une petite interface de type scikit-learn.\"\"\"\n", "\n", " def __init__(\n", " self,\n", " max_depth=None,\n", " min_samples_split=2,\n", " min_samples_leaf=1,\n", " ):\n", " self.max_depth = max_depth\n", " self.min_samples_split = min_samples_split\n", " self.min_samples_leaf = min_samples_leaf\n", "\n", " def fit(self, X, y):\n", " X = np.asarray(X, dtype=float)\n", " y = np.asarray(y)\n", " self._validate_training_data(X, y)\n", "\n", " self.classes_ = np.unique(y)\n", " self.n_features_in_ = X.shape[1]\n", " self.n_candidate_splits_ = 0\n", " self.tree_ = self._grow_tree(X, y, depth=0)\n", " return self\n", "\n", " def _grow_tree(self, X, y, depth):\n", " probabilities = class_probabilities(y, self.classes_)\n", " node = Node(\n", " probabilities=probabilities,\n", " n_samples=len(y),\n", " loss=entropy(y, self.classes_),\n", " )\n", "\n", " depth_limit = self.max_depth is not None and depth >= self.max_depth\n", " pure_node = np.count_nonzero(probabilities) == 1\n", " too_small = len(y) < self.min_samples_split\n", "\n", " if pure_node or depth_limit or too_small:\n", " return node\n", "\n", " split, n_candidates = find_best_split(\n", " X, y, self.classes_, self.min_samples_leaf\n", " )\n", " self.n_candidate_splits_ += n_candidates\n", " if split is None:\n", " return node\n", "\n", " node.feature, node.threshold, go_left = split\n", " node.left = self._grow_tree(X[go_left], y[go_left], depth + 1)\n", " node.right = self._grow_tree(X[~go_left], y[~go_left], depth + 1)\n", " return node\n", "\n", " def _find_leaf(self, x):\n", " node = self.tree_\n", " while not node.is_leaf:\n", " if x[node.feature] <= node.threshold:\n", " node = node.left\n", " else:\n", " node = node.right\n", " return node\n", "\n", " def predict_proba(self, X):\n", " X = self._validate_prediction_data(X)\n", " return np.vstack([self._find_leaf(x).probabilities for x in X])\n", "\n", " def predict(self, X):\n", " probabilities = self.predict_proba(X)\n", " return self.classes_[np.argmax(probabilities, axis=1)]\n", "\n", " def score(self, X, y):\n", " return float(np.mean(self.predict(X) == np.asarray(y)))\n", "\n", " def export_text(self, feature_names=None):\n", " if feature_names is None:\n", " feature_names = [f\"x[{j}]\" for j in range(self.n_features_in_)]\n", " if len(feature_names) != self.n_features_in_:\n", " raise ValueError(\"feature_names doit correspondre au nombre d'attributs\")\n", "\n", " lines = []\n", "\n", " def visit(node, indent):\n", " if node.is_leaf:\n", " prediction = self.classes_[np.argmax(node.probabilities)]\n", " if isinstance(prediction, np.generic):\n", " prediction = prediction.item()\n", " probabilities = np.round(node.probabilities, 3)\n", " lines.append(\n", " f\"{indent}prédire {prediction!r} \"\n", " f\"(p={probabilities}, n={node.n_samples})\"\n", " )\n", " return\n", "\n", " name = feature_names[node.feature]\n", " lines.append(f\"{indent}si {name} <= {node.threshold:.3f} :\")\n", " visit(node.left, indent + \" \")\n", " lines.append(f\"{indent}sinon :\")\n", " visit(node.right, indent + \" \")\n", "\n", " visit(self.tree_, \"\")\n", " return \"\\n\".join(lines)\n", "\n", " def _validate_training_data(self, X, y):\n", " if X.ndim != 2 or y.ndim != 1 or len(X) != len(y):\n", " raise ValueError(\n", " \"X doit être 2D et y doit être 1D, avec le même nombre de lignes\"\n", " )\n", " if len(y) == 0:\n", " raise ValueError(\"le jeu d'entraînement ne peut pas être vide\")\n", " if not np.isfinite(X).all():\n", " raise ValueError(\n", " \"les valeurs manquantes ou non finies ne sont pas prises en charge\"\n", " )\n", " if self.max_depth is not None and self.max_depth < 0:\n", " raise ValueError(\"max_depth doit être positif ou nul, ou None\")\n", " if self.min_samples_split < 2:\n", " raise ValueError(\"min_samples_split doit être au moins 2\")\n", " if self.min_samples_leaf < 1:\n", " raise ValueError(\"min_samples_leaf doit être au moins 1\")\n", "\n", " def _validate_prediction_data(self, X):\n", " if not hasattr(self, \"tree_\"):\n", " raise ValueError(\"appelez fit avant d'effectuer des prédictions\")\n", " X = np.asarray(X, dtype=float)\n", " if X.ndim == 1:\n", " X = X.reshape(1, -1)\n", " if X.ndim != 2 or X.shape[1] != self.n_features_in_:\n", " raise ValueError(\"X n'a pas le bon nombre d'attributs\")\n", " if not np.isfinite(X).all():\n", " raise ValueError(\n", " \"les valeurs manquantes ou non finies ne sont pas prises en charge\"\n", " )\n", " return X" ], "id": "classifier" }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Entraînement\n", "\n", "Nous limitons l’arbre à deux décisions sur tout chemin et exigeons que\n", "chaque feuille contienne au moins cinq exemples d’entraînement." ], "id": "5e58f657-9024-4cbf-8c45-91cdd1b8f81b" }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Exactitude sur le jeu de test : 1.000\n", "Divisions candidates évaluées : 312\n", "Ordre des classes : ['Gentoo' 'Pas Gentoo']\n", "\n", "Règles apprises :\n", "\n", "si bill_depth_mm <= 16.450 :\n", " si body_mass_g <= 3750.000 :\n", " prédire 'Pas Gentoo' (p=[0. 1.], n=5)\n", " sinon :\n", " prédire 'Gentoo' (p=[1. 0.], n=92)\n", "sinon :\n", " si body_mass_g <= 5100.000 :\n", " prédire 'Pas Gentoo' (p=[0. 1.], n=170)\n", " sinon :\n", " prédire 'Gentoo' (p=[1. 0.], n=6)" ] } ], "source": [ "tree_model = SimpleDecisionTreeClassifier(max_depth=2, min_samples_leaf=5)\n", "tree_model.fit(X_train, y_train)\n", "\n", "print(f\"Exactitude sur le jeu de test : {tree_model.score(X_test, y_test):.3f}\")\n", "print(f\"Divisions candidates évaluées : {tree_model.n_candidate_splits_}\")\n", "print(f\"Ordre des classes : {tree_model.classes_}\")\n", "print(\"\\nRègles apprises :\\n\")\n", "print(tree_model.export_text(feature_names))" ], "id": "training" }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Régions de décision\n", "\n", "Chaque test de cet arbre compare un attribut à un seuil. En deux\n", "dimensions, les régions obtenues sont donc délimitées par des frontières\n", "horizontales et verticales." ], "id": "5df8808b-605d-4cd4-8f11-c3fca7b82187" }, { "cell_type": "code", "execution_count": 11, "metadata": { "fig-height": 5, "fig-width": 9 }, "outputs": [ { "output_type": "display_data", "metadata": {}, "data": { "image/png": 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Rmc0zTz0ltRLPSeboMjIiNVFSa8WpRzzHcqw32safNsqiL76Q7lf2UM8rVqyo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} } ], "source": [ "def plot_decision_boundary(X, y, model, feature_names):\n", " x0 = np.linspace(X[:, 0].min() - 1, X[:, 0].max() + 1, 300)\n", " x1 = np.linspace(X[:, 1].min() - 200, X[:, 1].max() + 200, 300)\n", " xx0, xx1 = np.meshgrid(x0, x1)\n", "\n", " grid = np.column_stack([xx0.ravel(), xx1.ravel()])\n", " regions = np.argmax(\n", " model.predict_proba(grid), axis=1\n", " ).reshape(xx0.shape)\n", "\n", " plt.figure(figsize=(9, 5))\n", " plt.contourf(xx0, xx1, regions, alpha=0.25, cmap=\"Set2\")\n", " for label in model.classes_:\n", " selected = y == label\n", " plt.scatter(\n", " X[selected, 0],\n", " X[selected, 1],\n", " edgecolor=\"black\",\n", " label=label,\n", " )\n", " plt.xlabel(feature_names[0])\n", " plt.ylabel(feature_names[1])\n", " plt.title(\"Régions de classification de l'arbre de décision\")\n", " plt.legend()\n", " plt.tight_layout()\n", "\n", "\n", "plot_decision_boundary(X_train, y_train, tree_model, feature_names)\n", "plt.show()" ], "id": "cell-decision-regions" }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Complexité et limites\n", "\n", "Dans un nœud contenant $n$ exemples et $D$ attributs, cette\n", "implémentation évalue jusqu’à $D(n-1)$ seuils. Chaque évaluation\n", "parcourt de nouveau les exemples; la recherche d’une division demande\n", "donc approximativement $\\mathcal{O}(Dn^2)$ opérations. Les\n", "implémentations de production réutilisent les valeurs triées et des\n", "statistiques suffisantes pour éviter une grande partie de ce travail.\n", "\n", "Parmi les autres limites importantes :\n", "\n", "- seuls les attributs numériques et les divisions binaires par seuil\n", " sont pris en charge;\n", "- la recherche gloutonne ne garantit pas un arbre globalement optimal;\n", "- aucune stratégie pour les valeurs manquantes, aucune pondération des\n", " exemples et aucun élagage ne sont implémentés;\n", "- de petites modifications du jeu d’entraînement peuvent produire un\n", " arbre différent.\n", "\n", "# Expériences suggérées\n", "\n", "1. Modifiez `max_depth`, puis examinez les règles apprises et les\n", " régions de décision.\n", "2. Modifiez `min_samples_leaf` et observez quelles petites régions\n", " disparaissent.\n", "3. Utilisez les trois espèces plutôt que la cible binaire.\n", "4. Ajoutez un autre attribut numérique. Le classificateur fonctionnera\n", " encore, mais les régions de décision ne pourront plus être\n", " représentées dans une figure bidimensionnelle.\n", "5. Comparez les prédictions avec celles du `DecisionTreeClassifier` de\n", " scikit-learn en utilisant `criterion=\"entropy\"`." ], "id": "b74a12e5-8cf3-4a59-8209-04fb21153aba" } ], "nbformat": 4, "nbformat_minor": 5, "metadata": { "kernelspec": { "name": "python3", "display_name": "Python 3 (ipykernel)", "language": "python", "path": "/Users/turcotte/.virtualenvs/csi4106/share/jupyter/kernels/python3" } } }