{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "tp7-000",
   "metadata": {},
   "source": [
    "# Practical 7 — Decision trees and random forests\n",
    "\n",
    "**Objectives:** program impurity, split search, recursive fitting and tree traversal with\n",
    "NumPy; connect your implementation to scikit-learn; implement bootstrap aggregation;\n",
    "select and evaluate a tree and a random forest.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "tp7-001",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.datasets import load_breast_cancer, make_moons\n",
    "from sklearn.dummy import DummyClassifier, DummyRegressor\n",
    "from sklearn.ensemble import RandomForestClassifier, RandomForestRegressor\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.metrics import (accuracy_score, ConfusionMatrixDisplay, precision_score,\n",
    "                             recall_score, f1_score, roc_auc_score, root_mean_squared_error,\n",
    "                             mean_absolute_error, r2_score)\n",
    "from sklearn.model_selection import GridSearchCV, StratifiedKFold, KFold, train_test_split\n",
    "from sklearn.pipeline import make_pipeline\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.svm import SVC\n",
    "from sklearn.tree import DecisionTreeClassifier, DecisionTreeRegressor, plot_tree\n",
    "\n",
    "SEED = 42\n",
    "BLUE, RED = \"#2474b5\", \"#e30613\"\n",
    "plt.rcParams.update({\"figure.figsize\": (7, 4), \"font.size\": 11})\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "tp7-002",
   "metadata": {},
   "source": [
    "## 1. Learn the best split yourself — 15 min\n",
    "\n",
    "Implement `gini(y)` and `entropy(y)` using class proportions $p_k$:\n",
    "\n",
    "$$G(y)=1-\\sum_k p_k^2,\\qquad H(y)=-\\sum_{k:p_k>0}p_k\\log_2 p_k.$$\n",
    "\n",
    "Use `np.unique(y, return_counts=True)` to count classes. Check a pure group and\n",
    "an equally mixed binary group before using the eight observations below.\n",
    "\n",
    "Complete the four holes in `split_candidates`: the two child sizes, their weighted\n",
    "impurity $Q$, and the gain $I(y)-Q$, where\n",
    "\n",
    "$$Q=\\frac{n_L}{n}I(y_L)+\\frac{n_R}{n}I(y_R).$$\n",
    "\n",
    "The feature loop, candidate thresholds and routing mask are supplied. The thresholds\n",
    "are midpoints between distinct values, so both children contain observations.\n",
    "Each candidate is stored as a dictionary; a smaller score is better.\n",
    "\n",
    "1. Print each threshold, child sizes, score and gain, first with Gini, then entropy.\n",
    "2. Find the best threshold using `min(candidates, key=...)`.\n",
    "3. Which split would you keep? Do the criteria agree? Are the children pure?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "tp7-003",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x: [0.5 1.2 1.8 2.6 3.4 4.1 4.8 5.5]\n",
      "y: [0 0 0 0 1 1 0 1]\n"
     ]
    }
   ],
   "source": [
    "X_small = np.array([.5, 1.2, 1.8, 2.6, 3.4, 4.1, 4.8, 5.5])[:, None]\n",
    "y_small = np.array([0, 0, 0, 0, 1, 1, 0, 1])\n",
    "print(\"x:\", X_small[:, 0])\n",
    "print(\"y:\", y_small)\n",
    "\n",
    "# Provided helper: dispatch to your Gini or entropy function.\n",
    "def impurity(y, criterion=\"gini\"):\n",
    "    if criterion == \"gini\":\n",
    "        return gini(y)\n",
    "    if criterion == \"entropy\":\n",
    "        return entropy(y)\n",
    "    raise ValueError(\"Use gini or entropy\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "tp7-004",
   "metadata": {
    "tags": [
     "exercise"
    ]
   },
   "outputs": [],
   "source": [
    "# TODO: implement gini(y) and entropy(y) using NumPy.\n",
    "# TODO: test [0, 0, 0, 0] and [0, 0, 1, 1].\n",
    "\n",
    "def split_candidates(X, y, criterion=\"gini\"):\n",
    "    candidates = []\n",
    "    for j in range(X.shape[1]):\n",
    "        values = np.unique(X[:, j])\n",
    "        thresholds = (values[:-1] + values[1:]) / 2\n",
    "        for threshold in thresholds:\n",
    "            left = X[:, j] <= threshold  # True for observations sent to the left.\n",
    "            n_left = ...   # TODO: number of observations in the left child.\n",
    "            n_right = ...  # TODO: number of observations in the right child.\n",
    "            score = ...    # TODO: weighted child impurity, using impurity(..., criterion).\n",
    "            gain = ...     # TODO: parent impurity minus score.\n",
    "            candidates.append({\"feature\": j, \"threshold\": threshold,\n",
    "                               \"n_left\": n_left, \"n_right\": n_right,\n",
    "                               \"score\": score, \"gain\": gain})\n",
    "    return candidates\n",
    "\n",
    "# TODO: call split_candidates for each criterion and print the candidate values.\n",
    "# TODO: identify the candidate with the smallest score.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "tp7-005",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Labels: [0 0 0 0] Gini: 0.0 Entropy: -0.0\n",
      "Labels: [0 0 1 1] Gini: 0.5 Entropy: 1.0\n",
      "\n",
      "gini: threshold  left  right  score    gain\n",
      "             0.85     1      7  0.4286  0.0402\n",
      "             1.50     2      6  0.3750  0.0938\n",
      "             2.20     3      5  0.3000  0.1688\n",
      "             3.00     4      4  0.1875  0.2812\n",
      "             3.75     5      3  0.3667  0.1021\n",
      "             4.45     6      2  0.4583  0.0104\n",
      "             5.15     7      1  0.3571  0.1116\n",
      "Best threshold: 3.0 gain: 0.28125\n",
      "\n",
      "entropy: threshold  left  right  score    gain\n",
      "             0.85     1      7  0.8621  0.0924\n",
      "             1.50     2      6  0.7500  0.2044\n",
      "             2.20     3      5  0.6068  0.3476\n",
      "             3.00     4      4  0.4056  0.5488\n",
      "             3.75     5      3  0.7956  0.1589\n",
      "             4.45     6      2  0.9387  0.0157\n",
      "             5.15     7      1  0.7552  0.1992\n",
      "Best threshold: 3.0 gain: 0.5487949406953987\n"
     ]
    }
   ],
   "source": [
    "def gini(y):\n",
    "    _, counts = np.unique(y, return_counts=True)\n",
    "    p = counts / len(y)\n",
    "    return 1 - np.sum(p**2)\n",
    "\n",
    "def entropy(y):\n",
    "    _, counts = np.unique(y, return_counts=True)\n",
    "    p = counts / len(y)  # np.unique returns only observed classes, so p > 0.\n",
    "    return -np.sum(p * np.log2(p))\n",
    "\n",
    "def split_candidates(X, y, criterion=\"gini\"):\n",
    "    candidates = []\n",
    "    for j in range(X.shape[1]):\n",
    "        values = np.unique(X[:, j])\n",
    "        thresholds = (values[:-1] + values[1:]) / 2\n",
    "        for threshold in thresholds:\n",
    "            left = X[:, j] <= threshold\n",
    "            n_left, n_right = left.sum(), (~left).sum()\n",
    "            score = (n_left * impurity(y[left], criterion)\n",
    "                     + n_right * impurity(y[~left], criterion)) / len(y)\n",
    "            gain = impurity(y, criterion) - score\n",
    "            candidates.append({\"feature\": j, \"threshold\": threshold,\n",
    "                               \"n_left\": n_left, \"n_right\": n_right,\n",
    "                               \"score\": score, \"gain\": gain})\n",
    "    return candidates  # An empty list means that no split is valid.\n",
    "\n",
    "for labels in [np.array([0, 0, 0, 0]), np.array([0, 0, 1, 1])]:\n",
    "    print(\"Labels:\", labels, \"Gini:\", gini(labels), \"Entropy:\", entropy(labels))\n",
    "for criterion in [\"gini\", \"entropy\"]:\n",
    "    candidates = split_candidates(X_small, y_small, criterion)\n",
    "    print(f\"\\n{criterion}: threshold  left  right  score    gain\")\n",
    "    for split in candidates:\n",
    "        print(f\"{split['threshold']:17.2f} {split['n_left']:5d} {split['n_right']:6d} {split['score']:7.4f} {split['gain']:7.4f}\")\n",
    "    best = min(candidates, key=lambda split: split[\"score\"])\n",
    "    print(\"Best threshold:\", best[\"threshold\"], \"gain:\", best[\"gain\"])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "tp7-006",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "source": [
    "A pure group has Gini and entropy 0. For balanced binary labels, Gini is 0.5\n",
    "and entropy (base 2) is 1. Both criteria select threshold 3.0 here. The left\n",
    "child has four zeros; the right has three ones and one zero, so it is not pure.\n",
    "Gini's weighted score is 0.1875, with gain 0.28125. The scales differ between\n",
    "criteria; compare candidate scores within each criterion, not across criteria.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "tp7-007",
   "metadata": {},
   "source": [
    "## 2. Fit and traverse a small tree — 20 min\n",
    "\n",
    "Generate 80 random points in [0,6]² with a fixed seed. Class 1 occupies the upper-right\n",
    "corner: x1>3 and x2>3. Plot the data before fitting.\n",
    "\n",
    "Complete the skeleton below to build a binary tree with NumPy:\n",
    "\n",
    "1. At a node, call `split_candidates`, keep the smallest score, and split the data.\n",
    "2. Call `fit_manual` on each child. Stop at `max_depth`, at a pure node, or if no\n",
    "   positive-gain split is possible. These stopping rules are supplied.\n",
    "3. For prediction, follow the tests until a leaf, then return its class-1 proportion.\n",
    "\n",
    "The tree is a nested dictionary: leaves store `proba`; internal nodes also store\n",
    "`feature`, `threshold`, `left` and `right`. Classify with `proba > .5` (ties give 0).\n",
    "Compare depth 1 and depth 2, then follow the points (4,1) and (4,5).\n",
    "Why does the second split help? Why are learned thresholds not necessarily exactly 3?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "tp7-008",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.default_rng(SEED)\n",
    "X_toy = rng.uniform(0, 6, size=(80, 2))\n",
    "y_toy = ((X_toy[:, 0] > 3) & (X_toy[:, 1] > 3)).astype(int)\n",
    "for label, color in [(0, BLUE), (1, RED)]:\n",
    "    plt.scatter(*X_toy[y_toy == label].T, color=color, label=f\"Class {label}\")\n",
    "plt.xlabel(\"x1\")\n",
    "plt.ylabel(\"x2\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "def show_regions(ax, score_function, X, y, title):\n",
    "    low, high = X.min(axis=0) - .6, X.max(axis=0) + .6\n",
    "    xx, yy = np.meshgrid(np.linspace(low[0], high[0], 120),\n",
    "                         np.linspace(low[1], high[1], 120))\n",
    "    p = score_function(np.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape)\n",
    "    ax.contourf(xx, yy, p > .5, levels=[-.5, .5, 1.5], colors=[BLUE, RED], alpha=.15)\n",
    "    for label, color in [(0, BLUE), (1, RED)]:\n",
    "        ax.scatter(*X[y == label].T, color=color, edgecolors=\"white\", label=f\"Class {label}\")\n",
    "    ax.set(xlabel=\"$x_1$\", ylabel=\"$x_2$\", title=title)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "tp7-009",
   "metadata": {
    "tags": [
     "exercise"
    ]
   },
   "outputs": [],
   "source": [
    "def fit_manual(X, y, max_depth=2, criterion=\"gini\", depth=0):\n",
    "    node = {\"proba\": float(np.mean(y))}\n",
    "    if depth >= max_depth or impurity(y, criterion) < 1e-12:\n",
    "        return node\n",
    "    candidates = split_candidates(X, y, criterion)\n",
    "    if not candidates:\n",
    "        return node\n",
    "    # TODO: best = candidate with the smallest score.\n",
    "    # If best[\"gain\"] <= 1e-12, return node.\n",
    "    # TODO: obtain feature j and threshold, then create the left boolean mask.\n",
    "    # TODO: add feature, threshold, left and right to node.\n",
    "    # The children are calls to fit_manual on the corresponding subsets, depth+1.\n",
    "    return node\n",
    "\n",
    "def predict_proba_manual(tree, X):\n",
    "    probabilities = []\n",
    "    for x in X:\n",
    "        node = tree\n",
    "        # TODO: while \"feature\" in node, follow the left or right child.\n",
    "        probabilities.append(node[\"proba\"])\n",
    "    return np.array(probabilities)\n",
    "\n",
    "# TODO: fit depth 1 and depth 2; print training accuracy and draw regions with show_regions.\n",
    "# TODO: predict for np.array([[4., 1.], [4., 5.]]).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "tp7-010",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Depth 1 training accuracy: 0.8125\n",
      "Depth 2 training accuracy: 1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Query probabilities: [0. 1.]\n"
     ]
    }
   ],
   "source": [
    "def fit_manual(X, y, max_depth=2, criterion=\"gini\", depth=0):\n",
    "    node = {\"proba\": float(np.mean(y))}\n",
    "    if depth >= max_depth or impurity(y, criterion) < 1e-12:\n",
    "        return node\n",
    "    candidates = split_candidates(X, y, criterion)\n",
    "    if not candidates:\n",
    "        return node\n",
    "    best = min(candidates, key=lambda split: split[\"score\"])\n",
    "    if best[\"gain\"] <= 1e-12:\n",
    "        return node\n",
    "    j, threshold = int(best[\"feature\"]), float(best[\"threshold\"])\n",
    "    left = X[:, j] <= threshold\n",
    "    node.update(feature=j, threshold=threshold,\n",
    "                left=fit_manual(X[left], y[left], max_depth, criterion, depth+1),\n",
    "                right=fit_manual(X[~left], y[~left], max_depth, criterion, depth+1))\n",
    "    return node\n",
    "\n",
    "def predict_proba_manual(tree, X):\n",
    "    probabilities = []\n",
    "    for x in X:\n",
    "        node = tree\n",
    "        while \"feature\" in node:\n",
    "            side = \"left\" if x[node[\"feature\"]] <= node[\"threshold\"] else \"right\"\n",
    "            node = node[side]\n",
    "        probabilities.append(node[\"proba\"])\n",
    "    return np.array(probabilities)\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(10, 4))\n",
    "for ax, depth in zip(axes, [1, 2]):\n",
    "    tree = fit_manual(X_toy, y_toy, max_depth=depth)\n",
    "    p = predict_proba_manual(tree, X_toy)\n",
    "    print(\"Depth\", depth, \"training accuracy:\", accuracy_score(y_toy, p > .5))\n",
    "    show_regions(ax, lambda Z: predict_proba_manual(tree, Z), X_toy, y_toy, f\"Manual depth {depth}\")\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "manual_tree = fit_manual(X_toy, y_toy)\n",
    "queries = np.array([[4., 1.], [4., 5.]])\n",
    "print(\"Query probabilities:\", predict_proba_manual(manual_tree, queries))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "tp7-011",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "source": [
    "With seed 42, training accuracy rises from 0.8125 (depth 1) to 1.0 (depth 2).\n",
    "The root splits x1 near 3.33, then its right child splits x2 near 3.11.\n",
    "The two query probabilities are 0 and 1. Both variables are searched again at\n",
    "an internal node; the second test separates the classes remaining on the right.\n",
    "Candidate thresholds are midpoints of sampled values, so they need not equal\n",
    "the generating threshold 3. Perfect fit on these noiseless observations does not\n",
    "prove that every unseen point near the true boundary will be classified correctly.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "tp7-012",
   "metadata": {},
   "source": [
    "## 3. Connect the implementation to scikit-learn — 10 min\n",
    "\n",
    "1. Fit `DecisionTreeClassifier(max_depth=2, random_state=SEED)` on `X_toy, y_toy`.\n",
    "   Draw it with `plot_tree` and compare its predictions with your manual tree.\n",
    "2. Fit a stump (`max_depth=1`) on `X_small, y_small`. Does its threshold agree with Section 1?\n",
    "3. On the noisy moons split below, compare depths 1, 3 and None. Print training\n",
    "   accuracy, validation accuracy and leaf count; draw the training-data regions.\n",
    "\n",
    "Does a better training score imply a better validation score? Use no scaling for\n",
    "these trees. The moons experiment is independent of the later benchmark.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "tp7-013",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_moons, y_moons = make_moons(n_samples=240, noise=.25, random_state=SEED)\n",
    "X_fit, X_val, y_fit, y_val = train_test_split(\n",
    "    X_moons, y_moons, test_size=.3, stratify=y_moons, random_state=SEED)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "tp7-014",
   "metadata": {
    "tags": [
     "exercise"
    ]
   },
   "outputs": [],
   "source": [
    "# TODO: fit the simple sklearn tree on X_toy/y_toy, then plot_tree.\n",
    "# TODO: compare its predictions with predict_proba_manual(manual_tree, X_toy) > .5.\n",
    "# TODO: inspect the stump's tree_.threshold[0] on X_small/y_small.\n",
    "# TODO: compare depths 1, 3, None on X_fit/y_fit; print scores and leaf counts.\n",
    "# Use show_regions with lambda Z: model.predict_proba(Z)[:, 1].\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "tp7-015",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Toy probabilities agree: True\n",
      "sklearn stump threshold: 3.0\n",
      "  Depth  Leaves   Train acc.   Valid acc.\n",
      "      1       2       0.7976       0.7778\n",
      "      3       6       0.8929       0.8889\n",
      "   None      25       1.0000       0.9167\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1300x350 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "toy_tree = DecisionTreeClassifier(max_depth=2, random_state=SEED).fit(X_toy, y_toy)\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "plot_tree(toy_tree, feature_names=[\"x1\", \"x2\"], class_names=[\"0\", \"1\"], filled=True, ax=ax)\n",
    "plt.show()\n",
    "print(\"Toy probabilities agree:\", np.allclose(\n",
    "    toy_tree.predict_proba(X_toy)[:, 1], predict_proba_manual(manual_tree, X_toy)))\n",
    "stump = DecisionTreeClassifier(max_depth=1, random_state=SEED).fit(X_small, y_small)\n",
    "print(\"sklearn stump threshold:\", stump.tree_.threshold[0])\n",
    "fig, axes = plt.subplots(1, 3, figsize=(13, 3.5))\n",
    "print(f\"{'Depth':>7} {'Leaves':>7} {'Train acc.':>12} {'Valid acc.':>12}\")\n",
    "for ax, depth in zip(axes, [1, 3, None]):\n",
    "    model = DecisionTreeClassifier(max_depth=depth, random_state=SEED).fit(X_fit, y_fit)\n",
    "    print(f\"{str(depth):>7} {model.get_n_leaves():7d} {model.score(X_fit, y_fit):12.4f} {model.score(X_val, y_val):12.4f}\")\n",
    "    show_regions(ax, lambda Z: model.predict_proba(Z)[:, 1], X_fit, y_fit, f\"Depth {depth}\")\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "tp7-016",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "source": [
    "Both trees agree on the controlled sample, and sklearn finds stump threshold 3.0\n",
    "on the one-dimensional data. Tied candidates may be resolved differently in general.\n",
    "On the noisy moons, training accuracy reaches 1 for an unrestricted tree, while\n",
    "validation accuracy stays below 1. Additional depth can fit noise; its benefit\n",
    "must be checked on observations excluded from fitting.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "tp7-017",
   "metadata": {},
   "source": [
    "## 4. Program bootstrap aggregation, then use a random forest — 15 min\n",
    "\n",
    "Keep the moons training/validation split. Complete the three holes below:\n",
    "\n",
    "1. Draw n=len(y) indices **with replacement** using `rng.integers(0, n, size=n)`.\n",
    "   For example, `np.random.default_rng(0).integers(0, 5, size=5)` gives `[4, 3, 2, 1, 1]`:\n",
    "   observation 1 appears twice and observation 0 is omitted.\n",
    "2. Fit one `DecisionTreeClassifier` on the indexed observations. The surrounding\n",
    "   loop and storage of trees and sample indices are supplied.\n",
    "3. Average class-1 probabilities over trees with `np.mean(..., axis=0)`. The helper\n",
    "   below extracts the right probability column, including single-class trees.\n",
    "   For one observation, probabilities [.2, .7, .9] give .6, hence class 1.\n",
    "\n",
    "Run the supplied comparison cell after completing the functions. Compare the\n",
    "validation scores and boundaries of bagging and a random forest. What extra\n",
    "randomness does the forest add, and when is the feature subset sampled?\n",
    "\n",
    "The ensemble predicts class 1 when the mean probability exceeds .5. This can\n",
    "produce a different result from a majority vote over hard class predictions.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "tp7-bagging-probability-helper",
   "metadata": {},
   "outputs": [],
   "source": [
    "def class_one_probability(model, X):\n",
    "    # predict_proba columns follow model.classes_, not a fixed column number.\n",
    "    column = np.flatnonzero(model.classes_ == 1)\n",
    "    if not len(column):\n",
    "        # A tree trained without class 1 assigns it probability zero.\n",
    "        return np.zeros(len(X))\n",
    "    # If class 1 is the only class, its single column contains ones.\n",
    "    return model.predict_proba(X)[:, column[0]]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "tp7-018",
   "metadata": {
    "tags": [
     "exercise"
    ]
   },
   "outputs": [],
   "source": [
    "def fit_bagging(X, y, B=40, seed=SEED):\n",
    "    rng = np.random.default_rng(seed)  # Reproducible bootstrap draws.\n",
    "    trees, samples = [], []\n",
    "    n = len(y)\n",
    "    for b in range(B):\n",
    "        indices = ...  # TODO: draw n indices in [0, n), with replacement.\n",
    "        tree = DecisionTreeClassifier(random_state=seed+b)\n",
    "        # TODO: fit tree on X[indices] and y[indices].\n",
    "        trees.append(tree)\n",
    "        samples.append(indices)  # Retain duplicates: this is the bootstrap sample.\n",
    "    return trees, samples\n",
    "\n",
    "def bagging_probability(X):\n",
    "    # Shape: (number of trees, number of observations).\n",
    "    probabilities = np.array([class_one_probability(tree, X) for tree in bagged_trees])\n",
    "    return ...  # TODO: average over trees, returning one probability per observation.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "tp7-019",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [],
   "source": [
    "def fit_bagging(X, y, B=40, seed=SEED):\n",
    "    rng = np.random.default_rng(seed)\n",
    "    trees, samples = [], []\n",
    "    n = len(y)\n",
    "    for b in range(B):\n",
    "        indices = rng.integers(0, n, size=n)\n",
    "        tree = DecisionTreeClassifier(random_state=seed+b)\n",
    "        tree.fit(X[indices], y[indices])\n",
    "        trees.append(tree)\n",
    "        samples.append(indices)\n",
    "    return trees, samples\n",
    "\n",
    "def bagging_probability(X):\n",
    "    probabilities = np.array([class_one_probability(tree, X) for tree in bagged_trees])\n",
    "    return np.mean(probabilities, axis=0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "tp7-bagging-comparison",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean unique bootstrap observations: 105.65 of 168\n",
      "Bagging validation accuracy: 0.9305555555555556\n",
      "Forest validation accuracy: 0.9444444444444444\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Run after completing fit_bagging and bagging_probability above.\n",
    "bagged_trees, samples = fit_bagging(X_fit, y_fit)\n",
    "\n",
    "# sklearn's forest additionally randomizes candidate features at every node.\n",
    "forest_moons = RandomForestClassifier(n_estimators=100, max_features=\"sqrt\", random_state=SEED).fit(X_fit, y_fit)\n",
    "# Duplicates reduce the number of distinct observations in each sample.\n",
    "print(\"Mean unique bootstrap observations:\", np.mean([len(np.unique(i)) for i in samples]), \"of\", len(y_fit))\n",
    "# Average probabilities, then apply the binary classification threshold.\n",
    "print(\"Bagging validation accuracy:\", accuracy_score(y_val, bagging_probability(X_val) > .5))\n",
    "print(\"Forest validation accuracy:\", forest_moons.score(X_val, y_val))\n",
    "# Plot predictions in input space using the already-provided helper.\n",
    "fig, axes = plt.subplots(1, 2, figsize=(10, 4))\n",
    "show_regions(axes[0], bagging_probability, X_fit, y_fit, \"Manual bootstrap aggregation\")\n",
    "show_regions(axes[1], lambda Z: class_one_probability(forest_moons, Z), X_fit, y_fit, \"Random forest\")\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "tp7-020",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "source": [
    "Bootstrap samples contain duplicates and omit some training observations; the\n",
    "number of unique observations is smaller than the sample size. For B large,\n",
    "averaging tends to stabilize an unstable tree. A random forest additionally samples\n",
    "candidate features at each node, then searches for the best split among them.\n",
    "One validation split does not prove that either ensemble always wins.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "tp7-021",
   "metadata": {},
   "source": [
    "## 5. Select models on development data — 20 min\n",
    "\n",
    "Use the breast-cancer dataset from TP4/TP5: malignant +1, benign -1, same stratified\n",
    "20% test split and seed 42. Keep the test set unused until Section 6.\n",
    "\n",
    "Compare five procedures using the same three CV folds and mean **ROC-AUC**:\n",
    "\n",
    "| Procedure | Parameters to search |\n",
    "|---|---|\n",
    "| DummyClassifier(strategy=\"prior\") | no parameters |\n",
    "| StandardScaler + LogisticRegression(max_iter=3000) | C in [.1, 1, 10] |\n",
    "| StandardScaler + SVC(kernel=\"rbf\") | C in [.1, 1, 10], gamma in [\"scale\", .01, .1] |\n",
    "| DecisionTreeClassifier | criterion in [\"gini\", \"entropy\"], max_depth in [3, None], min_samples_leaf in [1, 5] |\n",
    "| RandomForestClassifier(n_estimators=100) | max_features in [\"sqrt\", 1.0], min_samples_leaf in [1, 5] |\n",
    "\n",
    "1. Run `GridSearchCV` with `return_train_score=True`, `n_jobs=1` and fixed tree seeds.\n",
    "2. Print mean train/CV AUC, CV standard deviation and selected parameters for each model.\n",
    "   Select `winner` by CV only. For SVM, AUC uses `decision_function`; `probability=True` is unnecessary.\n",
    "3. Plot the selected forest's ten largest `feature_importances_` values using NumPy and matplotlib.\n",
    "\n",
    "Why keep scaling inside the logistic and SVM pipelines? What changes with\n",
    "`max_features=1.0`? Can correlated variables share importance? Is importance causal?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "tp7-022",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Development: (455, 30) test: (114, 30)\n",
      "Development class counts: {np.int64(-1): np.int64(285), np.int64(1): np.int64(170)}\n"
     ]
    }
   ],
   "source": [
    "data = load_breast_cancer()\n",
    "X = data.data\n",
    "y = np.where(data.target == 0, 1, -1)\n",
    "X_dev, X_test, y_dev, y_test = train_test_split(\n",
    "    X, y, test_size=.2, stratify=y, random_state=SEED)\n",
    "cv = StratifiedKFold(3, shuffle=True, random_state=SEED)\n",
    "print(\"Development:\", X_dev.shape, \"test:\", X_test.shape)\n",
    "print(\"Development class counts:\", dict(zip(*np.unique(y_dev, return_counts=True))))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "tp7-023",
   "metadata": {
    "tags": [
     "exercise"
    ]
   },
   "outputs": [],
   "source": [
    "# TODO: define specs = {name: (estimator, parameter_grid)} for the five procedures.\n",
    "# TODO: run GridSearchCV on X_dev/y_dev and store the fitted searches in searches.\n",
    "# TODO: store results as a list of dictionaries; print the comparison and select winner by CV.\n",
    "# TODO: use np.argsort and plt.barh for the forest's ten largest MDI importances.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "tp7-024",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model       Train AUC     CV AUC     CV std  Parameters\n",
      "Logistic       0.9977     0.9955     0.0038  {'logisticregression__C': 1}\n",
      "SVM            0.9981     0.9946     0.0042  {'svc__C': 10, 'svc__gamma': 0.01}\n",
      "Forest         1.0000     0.9895     0.0034  {'max_features': 'sqrt', 'min_samples_leaf': 1}\n",
      "Tree           0.9886     0.9479     0.0146  {'criterion': 'gini', 'max_depth': 3, 'min_samples_leaf': 5}\n",
      "Dummy          0.5000     0.5000     0.0000  {}\n",
      "Frozen CV winner: Logistic\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "specs = {\n",
    "    \"Dummy\": (DummyClassifier(strategy=\"prior\"), {}),\n",
    "    \"Logistic\": (make_pipeline(StandardScaler(), LogisticRegression(max_iter=3000)),\n",
    "                 {\"logisticregression__C\": [.1, 1, 10]}),\n",
    "    \"SVM\": (make_pipeline(StandardScaler(), SVC(kernel=\"rbf\")),\n",
    "            {\"svc__C\": [.1, 1, 10], \"svc__gamma\": [\"scale\", .01, .1]}),\n",
    "    \"Tree\": (DecisionTreeClassifier(random_state=SEED),\n",
    "             {\"criterion\": [\"gini\", \"entropy\"], \"max_depth\": [3, None], \"min_samples_leaf\": [1, 5]}),\n",
    "    \"Forest\": (RandomForestClassifier(n_estimators=100, random_state=SEED, n_jobs=1),\n",
    "               {\"max_features\": [\"sqrt\", 1.0], \"min_samples_leaf\": [1, 5]}),\n",
    "}\n",
    "searches, rows = {}, []\n",
    "for name, (estimator, parameters) in specs.items():\n",
    "    search = GridSearchCV(estimator, parameters, cv=cv, scoring=\"roc_auc\",\n",
    "                          return_train_score=True, n_jobs=1).fit(X_dev, y_dev)\n",
    "    searches[name] = search\n",
    "    k = search.best_index_\n",
    "    rows.append({\"model\": name, \"train_auc\": search.cv_results_[\"mean_train_score\"][k],\n",
    "                 \"cv_auc\": search.best_score_, \"cv_std\": search.cv_results_[\"std_test_score\"][k],\n",
    "                 \"parameters\": search.best_params_})\n",
    "\n",
    "development_table = sorted(rows, key=lambda row: row[\"cv_auc\"], reverse=True)\n",
    "print(f\"{'Model':<10} {'Train AUC':>10} {'CV AUC':>10} {'CV std':>10}  Parameters\")\n",
    "for row in development_table:\n",
    "    print(f\"{row['model']:<10} {row['train_auc']:10.4f} {row['cv_auc']:10.4f} {row['cv_std']:10.4f}  {row['parameters']}\")\n",
    "winner = development_table[0][\"model\"]\n",
    "print(\"Frozen CV winner:\", winner)\n",
    "selected_forest = searches[\"Forest\"].best_estimator_\n",
    "importance = selected_forest.feature_importances_\n",
    "top = np.argsort(importance)[-10:]\n",
    "plt.barh(data.feature_names[top], importance[top], color=BLUE)\n",
    "plt.xlabel(\"Mean decrease in impurity (normalized)\")\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "tp7-025",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "source": [
    "Scaling is learned within each CV training fold for logistic regression and SVM.\n",
    "Trees need no standardization here. With max_features=1.0, all features are eligible\n",
    "at each node, while bootstrap remains. MDI sums weighted impurity reductions and\n",
    "normalizes the result. It describes the fitted model, not a causal mechanism;\n",
    "it can favor variables with many candidate cuts and share importance across\n",
    "correlated features. Fold standard deviations describe variability, not confidence\n",
    "intervals from independent experiments. SVM decision scores suffice for AUC.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "tp7-026",
   "metadata": {},
   "source": [
    "## 6. Final test-performance table and error analysis — 10 min\n",
    "\n",
    "Freeze all choices from Section 5. Evaluate each selected procedure once on the\n",
    "same test set. Print a table containing parameters, ROC-AUC, accuracy, malignant\n",
    "precision, malignant recall and malignant F1 (`pos_label=1`). Use `decision_function` for SVM AUC; for the other models, use the +1\n",
    "probability column located with `classes_`. Use `predict` for class metrics.\n",
    "\n",
    "Display the CV winner's confusion matrix with labels [-1, +1], and list the test-row\n",
    "indices of its false negatives. What is a false negative here? Do not change\n",
    "parameters or decision thresholds after inspecting test errors. Keep the CV winner\n",
    "even if another model has a larger test score.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "tp7-027",
   "metadata": {
    "tags": [
     "exercise"
    ]
   },
   "outputs": [],
   "source": [
    "# TODO: build test_table (a list of dictionaries) for the five frozen procedures.\n",
    "# Use decision_function for SVM; otherwise use class_one_probability.\n",
    "# TODO: print parameters, AUC, accuracy, malignant precision, recall and F1.\n",
    "# TODO: plot the CV winner's confusion matrix and print its false-negative indices.\n",
    "# TODO: interpret differences between AUC, recall and accuracy.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "tp7-028",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model          AUC   Accuracy  Precision   Recall       F1\n",
      "Dummy       0.5000     0.6316     0.0000   0.0000   0.0000\n",
      "  Parameters: {}\n",
      "Logistic    0.9960     0.9649     0.9750   0.9286   0.9512\n",
      "  Parameters: {'logisticregression__C': 1}\n",
      "SVM         0.9960     0.9825     1.0000   0.9524   0.9756\n",
      "  Parameters: {'svc__C': 10, 'svc__gamma': 0.01}\n",
      "Tree        0.9187     0.9123     0.9444   0.8095   0.8718\n",
      "  Parameters: {'criterion': 'gini', 'max_depth': 3, 'min_samples_leaf': 5}\n",
      "Forest      0.9929     0.9737     1.0000   0.9286   0.9630\n",
      "  Parameters: {'max_features': 'sqrt', 'min_samples_leaf': 1}\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False-negative test-row indices: [ 16  87 112]\n"
     ]
    }
   ],
   "source": [
    "rows = []\n",
    "for name, search in searches.items():\n",
    "    model = search.best_estimator_\n",
    "    predictions = model.predict(X_test)\n",
    "    scores = model.decision_function(X_test) if name == \"SVM\" else class_one_probability(model, X_test)\n",
    "    rows.append({\"model\": name, \"parameters\": search.best_params_,\n",
    "                 \"roc_auc\": roc_auc_score(y_test, scores), \"accuracy\": accuracy_score(y_test, predictions),\n",
    "                 \"precision\": precision_score(y_test, predictions, pos_label=1, zero_division=0),\n",
    "                 \"recall\": recall_score(y_test, predictions, pos_label=1, zero_division=0),\n",
    "                 \"f1\": f1_score(y_test, predictions, pos_label=1, zero_division=0)})\n",
    "test_table = rows\n",
    "print(f\"{'Model':<10} {'AUC':>7} {'Accuracy':>10} {'Precision':>10} {'Recall':>8} {'F1':>8}\")\n",
    "for row in test_table:\n",
    "    print(f\"{row['model']:<10} {row['roc_auc']:7.4f} {row['accuracy']:10.4f} {row['precision']:10.4f} {row['recall']:8.4f} {row['f1']:8.4f}\")\n",
    "    print(\"  Parameters:\", row[\"parameters\"])\n",
    "frozen_model = searches[winner].best_estimator_\n",
    "test_predictions = frozen_model.predict(X_test)\n",
    "ConfusionMatrixDisplay.from_predictions(y_test, test_predictions, labels=[-1, 1],\n",
    "    display_labels=[\"Benign (-1)\", \"Malignant (+1)\"], cmap=\"Blues\")\n",
    "plt.title(f\"CV-selected model: {winner}\")\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "print(\"False-negative test-row indices:\", np.flatnonzero((y_test == 1) & (test_predictions == -1)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "tp7-029",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "source": [
    "A false negative is a malignant observation classified as benign. Recall measures\n",
    "the fraction of malignant cases found, precision the fraction of malignant predictions\n",
    "that are correct, and AUC the quality of score ranking across thresholds. A high\n",
    "accuracy need not imply high malignant recall. This single test set gives uncertain\n",
    "estimates; it should not be used to select a new configuration.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "tp7-034",
   "metadata": {
    "tags": [
     "optional"
    ]
   },
   "source": [
    "## Optional — Trees and forests for regression\n",
    "\n",
    "Use the generated data below to predict a noisy continuous target.\n",
    "\n",
    "1. Fit a dummy regressor, a regression tree and a random forest. Select parameters\n",
    "   on development data with three-fold CV and `scoring=\"neg_root_mean_squared_error\"`.\n",
    "   Try tree `max_depth` in [2, 5, None] and `min_samples_leaf` in [1, 5]; for a\n",
    "   100-tree forest, try `min_samples_leaf` in [1, 5]. Select by the highest CV score\n",
    "   (the lowest RMSE). Keep the test data unused during selection.\n",
    "2. Print the selected parameters and positive CV RMSE, then freeze the choices.\n",
    "   Evaluate each selected regressor once on the test set: RMSE, MAE and R².\n",
    "3. Plot the fitted tree and forest predictions over a dense x-grid, together with\n",
    "   development observations and the noise-free function.\n",
    "\n",
    "What does a squared-error leaf predict? Why is a tree prediction piecewise constant?\n",
    "Does averaging trees remove all noise? What happens near the edges of the observed range?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "tp7-review-031",
   "metadata": {},
   "outputs": [],
   "source": [
    "rng_reg = np.random.default_rng(SEED)\n",
    "X_reg = rng_reg.uniform(-3, 3, size=(240, 1))\n",
    "def regression_signal(x):\n",
    "    return np.sin(2 * x) + .4 * x\n",
    "\n",
    "y_reg = regression_signal(X_reg[:, 0]) + rng_reg.normal(0, .3, len(X_reg))\n",
    "X_reg_dev, X_reg_test, y_reg_dev, y_reg_test = train_test_split(\n",
    "    X_reg, y_reg, test_size=.25, random_state=SEED)\n",
    "cv_reg = KFold(3, shuffle=True, random_state=SEED)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "tp7-review-032",
   "metadata": {
    "tags": [
     "exercise"
    ]
   },
   "outputs": [],
   "source": [
    "# TODO: GridSearchCV for DummyRegressor, DecisionTreeRegressor and RandomForestRegressor.\n",
    "# TODO: select by development CV; print selected parameters and positive CV RMSE.\n",
    "# TODO: print final test RMSE, MAE and R² for each selected regressor.\n",
    "# TODO: plot the two fitted prediction curves, development points and true signal.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "tp7-review-033",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dummy    CV RMSE=0.8120  {}\n",
      "Tree     CV RMSE=0.3544  {'max_depth': 5, 'min_samples_leaf': 5}\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Forest   CV RMSE=0.3330  {'min_samples_leaf': 5}\n",
      "Frozen regression CV winner: Forest\n",
      "Model       Test RMSE     Test MAE      Test R²\n",
      "Dummy          0.8529       0.7206      -0.0000\n",
      "Tree           0.3361       0.2765       0.8447\n",
      "Forest         0.3164       0.2604       0.8624\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "reg_specs = {\n",
    "    \"Dummy\": (DummyRegressor(strategy=\"mean\"), {}),\n",
    "    \"Tree\": (DecisionTreeRegressor(random_state=SEED),\n",
    "             {\"max_depth\": [2, 5, None], \"min_samples_leaf\": [1, 5]}),\n",
    "    \"Forest\": (RandomForestRegressor(n_estimators=100, random_state=SEED, n_jobs=1),\n",
    "               {\"min_samples_leaf\": [1, 5]}),\n",
    "}\n",
    "reg_searches = {}\n",
    "for name, (estimator, parameters) in reg_specs.items():\n",
    "    search = GridSearchCV(estimator, parameters, cv=cv_reg,\n",
    "                          scoring=\"neg_root_mean_squared_error\", n_jobs=1).fit(X_reg_dev, y_reg_dev)\n",
    "    reg_searches[name] = search\n",
    "    print(f\"{name:<8} CV RMSE={-search.best_score_:.4f}  {search.best_params_}\")\n",
    "reg_winner = max(reg_searches, key=lambda name: reg_searches[name].best_score_)\n",
    "print(\"Frozen regression CV winner:\", reg_winner)\n",
    "print(f\"{'Model':<8} {'Test RMSE':>12} {'Test MAE':>12} {'Test R²':>12}\")\n",
    "for name, search in reg_searches.items():\n",
    "    prediction = search.predict(X_reg_test)\n",
    "    print(f\"{name:<8} {root_mean_squared_error(y_reg_test, prediction):12.4f} {mean_absolute_error(y_reg_test, prediction):12.4f} {r2_score(y_reg_test, prediction):12.4f}\")\n",
    "\n",
    "x_plot = np.linspace(-3, 3, 400)[:, None]\n",
    "fig, axes = plt.subplots(1, 2, figsize=(11, 4))\n",
    "for ax, name in zip(axes, [\"Tree\", \"Forest\"]):\n",
    "    ax.scatter(X_reg_dev[:, 0], y_reg_dev, s=15, color=BLUE, alpha=.5, label=\"Development data\")\n",
    "    ax.plot(x_plot[:, 0], regression_signal(x_plot[:, 0]), color=\"black\", ls=\"--\", label=\"Noise-free signal\")\n",
    "    ax.plot(x_plot[:, 0], reg_searches[name].predict(x_plot), color=RED, label=\"Prediction\")\n",
    "    ax.set(xlabel=\"x\", ylabel=\"Target\", title=name)\n",
    "    ax.legend(fontsize=9)\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "tp7-review-034",
   "metadata": {
    "tags": [
     "correction"
    ]
   },
   "source": [
    "A squared-error leaf returns the mean target of its fitting observations. The tree\n",
    "is constant between learned thresholds; averaging trees combines different\n",
    "partitions and can reduce variance, while observation noise remains. Trees and\n",
    "forests do not extrapolate trends beyond the fitted input range: outside it,\n",
    "predictions remain those of the outer leaves. CV chooses the configuration before\n",
    "any test results are inspected. Negative RMSE scores are negated for readable output;\n",
    "RMSE and MAE use the target's units, whereas R² compares with a constant predictor.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6aab4de",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "insa-iml-practicals (3.10.20)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.20"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
