supervised_unsupervised.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 716,
   "id": "7cec0660-e52a-4c03-a21b-6026be8b215d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "from sklearn.datasets import make_classification\n",
    "from sklearn.metrics import (\n",
    "    classification_report,\n",
    "    precision_score,\n",
    "    recall_score,\n",
    "    accuracy_score,\n",
    ")\n",
    "from sklearn.linear_model import LogisticRegression, SGDClassifier\n",
    "from scipy.stats import gaussian_kde\n",
    "from scipy.stats._kde import gaussian_kde as TGaussianKDE\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from matplotlib_inline.backend_inline import set_matplotlib_formats\n",
    "set_matplotlib_formats(\"svg\")\n",
    "\n",
    "usr = os.path.expanduser(\"~\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 656,
   "id": "ee58b271-4844-409b-8ee8-ca23807e4283",
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = make_classification(\n",
    "    n_samples=400,\n",
    "    n_features=2,\n",
    "    n_informative=2,\n",
    "    n_redundant=0,\n",
    "    n_repeated=0,\n",
    "    n_classes=2,\n",
    "    random_state=42,\n",
    ")"
   ]
  },
  {
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   "execution_count": 733,
   "id": "cd53a148-c911-4a52-a99d-e48e69261b5f",
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 360x216 with 1 Axes>"
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     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplots(1, 1, figsize=(5, 3))\n",
    "for i, (label, color) in enumerate(\n",
    "    (\n",
    "        (\"negative\", \"#235d9c\"),\n",
    "        (\"positive\", \"#a40c2b\")\n",
    "    )\n",
    "):\n",
    "    mask = y == i\n",
    "    plt.scatter(\n",
    "        X[mask, 0], X[mask, 1], s=10, label=label, edgecolors=color, facecolors=\"none\")\n",
    "\n",
    "fig_path = os.path.join(\n",
    "    usr, \"Documents/site/assets/img/binary_problem.svg\"\n",
    ")\n",
    "plt.tight_layout()\n",
    "plt.legend()\n",
    "plt.savefig(fig_path, transparent=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 531,
   "id": "a40f60dc-2d01-4299-9ae6-4296ca19f594",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_with_y = np.column_stack([X, y])\n",
    "\n",
    "dist = gaussian_kde(X_with_y.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 618,
   "id": "4b1eb9c7-45df-46de-8b11-9df5b8a17092",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.07661607]\n",
      "[0.17057924]\n"
     ]
    }
   ],
   "source": [
    "marginal_dist = dist.marginal([0, 1])\n",
    "test = [ 0.8006456 ,  1.14226238]\n",
    "\n",
    "print(marginal_dist.pdf(test))\n",
    "print(dist.pdf(test + [0]) + dist.pdf(test + [1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 502,
   "id": "1acede23-e912-4603-996b-a8a6abd42d76",
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_mesh(X: np.array, y: np.array) -> tuple[np.array, np.array]:\n",
    "    x_min, y_min = X.min(axis=0).round() - 0.5\n",
    "    x_max, y_max = X.max(axis=0).round() + 0.5\n",
    "    xx, yy = np.meshgrid(\n",
    "        np.arange(x_min, x_max, 0.05),\n",
    "        np.arange(y_min, y_max, 0.05)\n",
    "    )\n",
    "    \n",
    "    return xx, yy  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 553,
   "id": "5b3e5891-4b4b-40f8-897a-03d1dd212b87",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_joint_pdf(X: np.array, y: np.array, dist: TGaussianKDE) -> None:\n",
    "    xx, yy = create_mesh(X, y) \n",
    "    n = xx.size\n",
    "    fig, ax = plt.subplots(1, 1, figsize=(5, 3))\n",
    "\n",
    "    X_pos = np.c_[xx.ravel(), yy.ravel(), np.ones(n)].T\n",
    "    X_neg = np.c_[xx.ravel(), yy.ravel(), np.zeros(n)].T\n",
    "    Z_pos = dist.pdf(X_pos)\n",
    "    Z_neg = dist.pdf(X_neg)\n",
    "    Z = Z_pos - Z_neg\n",
    "    Z = Z.reshape(xx.shape)\n",
    "        \n",
    "    ax.contour(xx, yy, Z, alpha=1, cmap=\"RdBu_r\")\n",
    "    for j, color in enumerate((\"#235d9c\", \"#a40c2b\")):\n",
    "        mask = y == j\n",
    "        ax.scatter(\n",
    "            X[mask, 0], X[mask, 1], s=10, edgecolors=color, facecolors=\"none\",\n",
    "        )\n",
    "        \n",
    "    ax.set_title(f\"Probabiltiy Density Function of $p(x,y)$\")\n",
    "    \n",
    "    fig_path = os.path.join(\n",
    "        usr, \"Documents/site/assets/img/joint_pdf.svg\"\n",
    "    )\n",
    "\n",
    "    plt.tight_layout()    \n",
    "    plt.savefig(fig_path, transparent=True)\n",
    "    plt.show()"
   ]
  },
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   "execution_count": 554,
   "id": "c7d397b9-675b-4fde-a8d1-aeabccc4bdb5",
   "metadata": {},
   "outputs": [
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    "plot_joint_pdf(X, y, dist)"
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   "id": "f49f8878-d598-4eec-85db-81276609b7e0",
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   "source": [
    "`KDEClassifier` implements\n",
    "\n",
    "$$\n",
    "p(y|x) = \\frac{p(x, y)}{\\sum_{\\forall y' \\in y}p(x, y')}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 767,
   "id": "77c43de2-1a10-4493-95d8-91256718f910",
   "metadata": {},
   "outputs": [],
   "source": [
    "class KDEClassifier:\n",
    "        \n",
    "    def fit(self, X: np.array, y: np.array) -> None:\n",
    "        X_with_y = np.column_stack([X, y])\n",
    "        self.dist = gaussian_kde(X_with_y.T)\n",
    "        \n",
    "    def predict_proba_density(self, X: np.array) -> np.array:\n",
    "        y_pos = np.ones(len(X))\n",
    "        y_neg = y_pos - 1\n",
    "        X_with_pos = np.column_stack([X, y_pos]).T\n",
    "        X_with_neg = np.column_stack([X, y_neg]).T\n",
    "        \n",
    "        proba_densities = [\n",
    "            self.dist.pdf(X_with_)\n",
    "            / (self.dist.pdf(X_with_neg) + self.dist.pdf(X_with_pos))\n",
    "            for X_with_ in (X_with_neg, X_with_pos)\n",
    "        ]\n",
    "        \n",
    "        return np.column_stack(proba_densities)\n",
    "    \n",
    "    def predict(self, X: np.array) -> np.array:\n",
    "        proba_densities = self.predict_proba_density(X)\n",
    "        return np.argmax(proba_densities, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 768,
   "id": "f885195c-11f4-4664-9a71-cbda8d4de69b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       0.92      0.93      0.93       201\n",
      "           1       0.93      0.92      0.92       199\n",
      "\n",
      "    accuracy                           0.93       400\n",
      "   macro avg       0.93      0.92      0.92       400\n",
      "weighted avg       0.93      0.93      0.92       400\n",
      "\n",
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       0.92      0.97      0.95       201\n",
      "           1       0.97      0.92      0.94       199\n",
      "\n",
      "    accuracy                           0.94       400\n",
      "   macro avg       0.95      0.94      0.94       400\n",
      "weighted avg       0.95      0.94      0.94       400\n",
      "\n"
     ]
    }
   ],
   "source": [
    "kde_classifier = KDEClassifier()\n",
    "kde_classifier.fit(X, y)\n",
    "\n",
    "lr_classifier = SGDClassifier(loss=\"log_loss\", random_state=0)\n",
    "lr_classifier.fit(X, y)\n",
    "\n",
    "print(classification_report(y, lr_classifier.predict(X)))\n",
    "print(classification_report(y, kde_classifier.predict(X)))"
   ]
  },
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   "cell_type": "code",
   "execution_count": 747,
   "id": "bed8f687-bea8-4cd7-a998-fbe1cff5cade",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_regions(\n",
    "    X: np.array,\n",
    "    y: np.array,\n",
    "    kde_classifier: KDEClassifier,\n",
    "    lr_classifier: SGDClassifier\n",
    ") -> None:\n",
    "    xx, yy = create_mesh(X, y)\n",
    "    n = xx.size\n",
    "    \n",
    "    fig, ax = plt.subplots(1, 2, figsize=(8, 4))\n",
    "    \n",
    "    for i, model in enumerate((kde_classifier, lr_classifier)):\n",
    "        \n",
    "        X_ = np.c_[xx.ravel(), yy.ravel()]\n",
    "        if isinstance(model, KDEClassifier):\n",
    "            model_name = \"KDE Classifier\"\n",
    "            Z = model.predict_proba_density(X_)[:, 0]\n",
    "        else:\n",
    "            model_name = \"Logistic Regression\"\n",
    "            Z = model.predict_proba(X_)[:, 1]\n",
    "        Z = Z.reshape(xx.shape)\n",
    "        \n",
    "        y_pred = model.predict(X)\n",
    "        metrics = (\n",
    "            f\"Precision = {precision_score(y, y_pred):.2f}\\n\"\n",
    "            f\"Recall = {recall_score(y, y_pred):.2f}\\n\"\n",
    "            f\"Accuracy = {accuracy_score(y, y_pred):.2f}\"\n",
    "        )\n",
    "        \n",
    "        ax[i].contour(xx, yy, Z, alpha=1, cmap='RdBu_r')\n",
    "        ax[i].text(\n",
    "            -3.2, -5, metrics,\n",
    "            bbox={\"boxstyle\": \"round\", \"facecolor\": \"none\"},\n",
    "            fontsize=8\n",
    "        )\n",
    "        for j, color in enumerate((\"#235d9c\", \"#a40c2b\")):\n",
    "            mask = y == j\n",
    "            ax[i].scatter(\n",
    "                X[mask, 0], X[mask, 1], s=10, edgecolors=color, facecolors=\"none\"\n",
    "            )\n",
    "        \n",
    "        ax[i].set_title(model_name)\n",
    "        \n",
    "    fig_path = os.path.join(\n",
    "        usr, \"Documents/site/assets/img/classifier_comparison.svg\"\n",
    "    )\n",
    "    plt.tight_layout()\n",
    "    plt.savefig(fig_path, transparent=True)\n",
    "    plt.show()"
   ]
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   "execution_count": 748,
   "id": "2d856db2-3af5-4b50-a534-a9656ba9e9f7",
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