notebooks/multiclass_classification.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c3e40814-c89e-4294-9240-19c08d5f22c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9ca4d044-fa32-4373-b56e-d7af4a529e98",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "sys.path.append(\"..\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "94d597ae-3203-44b9-8ce3-afcb98d7934f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((120, 4), (120,))"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load dataset\n",
    "\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "data = load_iris()\n",
    "X = StandardScaler().fit_transform(data[\"data\"])\n",
    "y = data[\"target\"]\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
    "\n",
    "X_train.shape, y_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "64e97e46-318b-4124-ba82-9ff911e6df49",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fd2f7afe220>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Build model\n",
    "\n",
    "from models.multiclass_logistic_regressor import MulticlassLogisticRegressor\n",
    "\n",
    "m = MulticlassLogisticRegressor().fit(X_train, y_train, n_iter=1000, eta=1.0e-3, lmd=0.5)\n",
    "\n",
    "# Learning curve\n",
    "# maximizing the log likelihood of the model\n",
    "plt.plot(m.loglik_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "54186ae3-8938-4023-b044-bf2148e0d2d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9666666666666667"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Accuracy score\n",
    "\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "y_hat = m.predict(X_test)\n",
    "accuracy_score(y_test, y_hat)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86f423cf-854a-4b9c-9125-4685a1e3a893",
   "metadata": {},
   "source": [
    "# Comparing to scikit-learn's implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "683145b4-a306-48fe-ba8b-45c7939fb0b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9333333333333333"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "s = LogisticRegression().fit(X_train, y_train)\n",
    "accuracy_score(y_test, s.predict(X_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8c213f29-b334-49c6-acf1-0b7327764803",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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p0sX/32FhYYqIiNDXX399sS/9gnCOCAAADgoODtbmzZv1+uuvq1OnTlq4cKGuvvpqHT58WJLUrl07dejQQc8991ylczn+V0lJiSRp+fLlysnJ8d8++ugj7dq1S5L07rvvatSoUfr5z3+uDRs2aN++fZo2bdpZJ6SGhYWdc4yGDRtWuu9yueT1ei/6tV8IjogAAOAwl8ulPn36qE+fPpoxY4YSEhK0du1aSdKVV16prKws9e3bV7/4xS/097///awgkKRmzZqpZcuW+uyzzzRq1KhzjrNz504lJCRo2rRp/mVHjx515kXVEEIEAAAHZWdna8uWLRo0aJBiY2OVnZ2tgoICdezYUR988IEkKTY2Vlu3blW/fv00cuRIrV69Wg0anP0rOj09XQ8//LAiIyM1ZMgQeTwe7d69W//+9781ceJEtW/fXp9//rlWr16tnj176rXXXvMHT11FiAAAAlsNXunUCREREdqxY4cWLFigoqIiJSQkaN68eRo6dKjWrFnjX6958+baunWr+vbtq1GjRmnVqlVnbev+++9XaGionnzySU2aNElhYWFKSkrShAkTJEm33HKLfvvb32r8+PHyeDwaNmyYHnvsMaWlpdXSq60+l+9/Pz9UhxQVFSkyMlKFhYVnnWgDBILWU1+znkJAOTJ7mPUUUId99913Onz4cKVrX8BOVX8f1fn9zcmqAADADCECAADMECIAAMAMIQIAAMwQIgCAgFKHP2NRr9TU3wMhAgAICGcu8nXq1CnjmUCS/2qt//2leReD64gAAAJCcHCwoqKi/N99EhoaKpfLZTyr+snr9aqgoEChoaHnvPBadRAiAICA0bx5c0ly/IvY8MOCgoLUqlWrS45BQgQAEDBcLpdatGih2NjYKr8gDs4LCQlRUNCln+FBiAAAAk5wcPAln5uAuoGTVQEAgBlCBAAAmCFEAACAGUIEAACYIUQAAIAZQgQAAJghRAAAgBlCBAAAmCFEAACAGUIEAACYIUQAAIAZQgQAAJghRAAAgBlCBAAAmCFEAACAGUIEAACYIUQAAIAZQgQAAJghRAAAgBlHQyQjI0M9e/ZUeHi4YmNjddttt+mTTz5xckgAABBAHA2Rf/7zn3rwwQe1a9cubd68WeXl5Ro0aJBKS0udHBYAAASIBk5u/I033qh0PzMzU7GxsdqzZ4/+7//+z8mhAQBAAHA0RP5XYWGhJCk6Ovqcj3s8Hnk8Hv/9oqKiWpkXAACwUWsnq3q9Xk2YMEF9+vTRNddcc851MjIyFBkZ6b/Fx8fX1vQAAICBWguRBx98UB999JFWr1593nVSU1NVWFjov+Xl5dXW9AAAgIFaeWtm/Pjx2rBhg3bs2KG4uLjzrud2u+V2u2tjSgAAoA5wNER8Pp8eeughrV27Vtu3b1ebNm2cHA4AAAQYR0PkwQcf1KpVq7R+/XqFh4fr+PHjkqTIyEg1btzYyaEBAEAAcPQckSVLlqiwsFB9+/ZVixYt/Lc1a9Y4OSwAAAgQjr81AwAAcD61eh0RALgkaZHWM6h9aYXWMwAcxZfeAQAAM4QIAAAwQ4gAAAAzhAgAADBDiAAAADOECAAAMEOIAAAAM4QIAAAwQ4gAAAAzhAgAADBDiAAAADOECAAAMEOIAAAAM4QIAAAwQ4gAAAAzhAgAADBDiAAAADOECAAAMEOIAAAAM4QIAAAwQ4gAAAAzhAgAADBDiAAAADOECAAAMEOIAAAAM4QIAAAwQ4gAAAAzhAgAADBDiAAAADOECAAAMEOIAAAAM4QIAAAwQ4gAAAAzhAgAADBDiAAAADOECAAAMEOIAAAAM4QIAAAwQ4gAAAAzhAgAADBDiAAAADOECAAAMEOIAAAAM4QIAAAwQ4gAAAAzhAgAADBDiAAAADOECAAAMEOIAAAAM4QIAAAwQ4gAAAAzhAgAADDjaIjs2LFDN998s1q2bCmXy6V169Y5ORwAAAgwjoZIaWmpunbtqsWLFzs5DAAACFANnNz40KFDNXToUCeHAAAAAczREKkuj8cjj8fjv19UVGQ4GwAA4LQ6dbJqRkaGIiMj/bf4+HjrKQEAAAfVqRBJTU1VYWGh/5aXl2c9JQAA4KA69daM2+2W2+22ngYAAKgldeqICAAAqF8cPSJSUlKi3Nxc//3Dhw8rJydH0dHRatWqlZNDAwCAAOBoiOzevVv9+vXz3584caIkKTk5WZmZmU4ODQAAAoCjIdK3b1/5fD4nhwAAAAGMc0QAAIAZQgQAAJghRAAAgBlCBAAAmCFEAACAGUIEAACYIUQAAIAZQgQAAJghRAAAgBlCBAAAmCFEAACAGUIEAACYIUQAAIAZQgQAAJghRAAAgBlCBAAAmCFEAACAGUIEAACYIUQAAIAZQgQAAJghRAAAgBlCBAAAmCFEAACAGUIEAACYIUQAAIAZQgQAAJghRAAAgBlCBAAAmCFEAACAGUIEAACYIUQAAIAZQgQAAJghRAAAgBlCBAAAmCFEAACAGUIEAACYIUQAAIAZQgQAAJghRAAAgBlCBAAAmCFEAACAGUIEAACYIUQAAIAZQgQAAJghRAAAgBlCBAAAmCFEAACAGUIEAACYIUQAAIAZQgQAAJghRAAAgBlCBAAAmCFEAACAmVoJkcWLF6t169Zq1KiRrr/+er333nu1MSwAAKjjHA+RNWvWaOLEiZo5c6b27t2rrl27avDgwfr666+dHhoAANRxjofIn/70J6WkpOjee+9Vp06d9Oyzzyo0NFTPPfec00MDAIA6ztEQKSsr0549ezRw4MD/DBgUpIEDB+rdd989a32Px6OioqJKNwAAcPlq4OTGv/nmG50+fVrNmjWrtLxZs2Y6ePDgWetnZGQoPT3dySlV0nrqa7U21uXgyOxhVa+QFlk7E6lL0gqrfPgH/8xQPT/w513f8DOs+vg5dg7G/67q1KdmUlNTVVhY6L/l5eVZTwkAADjI0SMiV155pYKDg/XVV19VWv7VV1+pefPmZ63vdrvldrudnBIAAKhDHD0iEhISoh49emjLli3+ZV6vV1u2bFGvXr2cHBoAAAQAR4+ISNLEiROVnJysa6+9Vtddd50WLFig0tJS3XvvvU4PDQAA6jjHQ+TOO+9UQUGBZsyYoePHj6tbt2564403zjqBFQAA1D+Oh4gkjR8/XuPHj6+NoQAAQACpU5+aAQAA9QshAgAAzBAiAADADCECAADM1MrJqqgnuPw2AKCaOCICAADMECIAAMAMIQIAAMwQIgAAwAwhAgAAzBAiAADADCECAADMECIAAMAMIQIAAMwQIgAAwAwhAgAAzBAiAADADCECAADMECIAAMAMIQIAAMwQIgAAwAwhAgAAzBAiAADADCECAADMECIAAMAMIQIAAMwQIgAAwAwhAgAAzBAiAADADCECAADMECIAAMAMIQIAAMwQIgAAwAwhAgAAzBAiAADADCECAADMNLCegKUjs4dZTwEAgHqNIyIAAMAMIQIAAMwQIgAAwAwhAgAAzBAiAADADCECAADMECIAAMAMIQIAAMwQIgAAwAwhAgAAzBAiAADADCECAADMECIAAMAMIQIAAMwQIgAAwAwhAgAAzDgWIrNmzVLv3r0VGhqqqKgop4YBAAABzLEQKSsr0x133KFx48Y5NQQAAAhwDZzacHp6uiQpMzPTqSEAAECAcyxELobH45HH4/HfLyoqMpwNAABwWp06WTUjI0ORkZH+W3x8vPWUAACAg6oVIlOnTpXL5arydvDgwYueTGpqqgoLC/23vLy8i94WAACo+6r11swjjzyi0aNHV7lO27ZtL3oybrdbbrf7op8PAAACS7VCJCYmRjExMU7NBQAA1DOOnaz6+eef68SJE/r88891+vRp5eTkSJISExPVpEkTp4YFAAABxLEQmTFjhp5//nn//e7du0uStm3bpr59+zo1LAAACCCOfWomMzNTPp/vrBsRAgAAzqhTH98FAAD1CyECAADMECIAAMAMIQIAAMwQIgAAwAwhAgAAzBAiAADADCECAADMECIAAMAMIQIAAMwQIgAAwAwhAgAAzBAiAADADCECAADMECIAAMAMIQIAAMwQIgAAwAwhAgAAzBAiAADADCECAADMECIAAMAMIQIAAMwQIgAAwAwhAgAAzBAiAADADCECAADMECIAAMAMIQIAAMwQIgAAwAwhAgAAzBAiAADADCECAADMECIAAMAMIQIAAMwQIgAAwAwhAgAAzBAiAADADCECAADMECIAAMAMIQIAAMw0sJ4AAAB1Rlqh9QzqHY6IAAAAM4QIAAAwQ4gAAAAzhAgAADBDiAAAADOECAAAMEOIAAAAM4QIAAAwQ4gAAAAzhAgAADBDiAAAADOECAAAMEOIAAAAM46FyJEjRzRmzBi1adNGjRs3Vrt27TRz5kyVlZU5NSQAAAgwDZza8MGDB+X1erV06VIlJibqo48+UkpKikpLSzV37lynhgUAAAHEsRAZMmSIhgwZ4r/ftm1bffLJJ1qyZAkhAgAAJDkYIudSWFio6Ojo8z7u8Xjk8Xj894uKimpjWgAAwEitnayam5urhQsXauzYseddJyMjQ5GRkf5bfHx8bU0PAAAYqHaITJ06VS6Xq8rbwYMHKz3nyy+/1JAhQ3THHXcoJSXlvNtOTU1VYWGh/5aXl1f9VwQAAAJGtd+aeeSRRzR69Ogq12nbtq3/v48dO6Z+/fqpd+/eWrZsWZXPc7vdcrvd1Z0SAAAIUNUOkZiYGMXExFzQul9++aX69eunHj166M9//rOCgrhsCQAA+A/HTlb98ssv1bdvXyUkJGju3LkqKCjwP9a8eXOnhgUAAAHEsRDZvHmzcnNzlZubq7i4uEqP+Xw+p4YFAAABxLH3SkaPHi2fz3fOGwAAgMR3zQAAAEOECAAAMEOIAAAAM4QIAAAwQ4gAAAAzhAgAADBDiAAAADOECAAAMEOIAAAAM45d4h0A4Kwjs4dZTwG4ZBwRAQAAZggRAABghhABAABmCBEAAGCGEAEAAGYIEQAAYIYQAQAAZggRAABghhABAABmCBEAAGCGEAEAAGYIEQAAYIYQAQAAZggRAABghhABAABmGlhPoCo+n0+SVFRUZDwTAABwoc783j7ze7wqdTpEiouLJUnx8fHGMwEAANVVXFysyMjIKtdx+S4kV4x4vV4dO3ZM4eHhcrlc1tOpFUVFRYqPj1deXp4iIiKsp4PLEPsYnMY+Bp/Pp+LiYrVs2VJBQVWfBVKnj4gEBQUpLi7OehomIiIi+AcMR7GPwWnsY/XbDx0JOYOTVQEAgBlCBAAAmCFE6hi3262ZM2fK7XZbTwWXKfYxOI19DNVRp09WBQAAlzeOiAAAADOECAAAMEOIAAAAM4QIAAAwQ4gAAAAzhEgAyc/P11133aWrrrpKQUFBmjBhgvWUcJnJysrSjTfeqJiYGEVERKhXr17atGmT9bRwmXj77bfVp08fXXHFFWrcuLE6dOig+fPnW08LxgiRAOLxeBQTE6Pp06era9eu1tPBZWjHjh268cYbtXHjRu3Zs0f9+vXTzTffrH379llPDZeBsLAwjR8/Xjt27NCBAwc0ffp0TZ8+XcuWLbOeGgxxHZFa4PV6NXfuXC1btkx5eXlq1qyZxo4dq2nTpl30Nvv27atu3bppwYIFNTdRBCwn9rEzOnfurDvvvFMzZsyogZkiEDm5f40YMUJhYWH6y1/+UgMzRSCq0196d7lITU3V8uXLNX/+fP30pz9Vfn6+Dh48KOn7H/JHjx4973N/9rOf6fXXX6+tqSJAObWPeb1eFRcXKzo62pF5IzA4tX/t27dPO3fu1OOPP+7IvBEYOCLisOLiYsXExGjRokW6//77z3r86NGjKi8vP+/zGzdurB/96EdnLeeICM5wah+TpDlz5mj27Nk6ePCgYmNja2zOCBxO7F9xcXEqKChQRUWF0tLS9Nhjj9X4vBE4OCLisAMHDsjj8WjAgAHnfDwhIaGWZ4TLjVP72KpVq5Senq7169cTIfWYE/vXW2+9pZKSEu3atUtTp05VYmKiRo4cealTRYAiRBzWuHHjKh/nrRlcKif2sdWrV+v+++/XSy+9pIEDB9bIPBGYnNi/2rRpI0lKSkrSV199pbS0NEKkHiNEHNa+fXs1btxYW7ZsOedhzY0bN/7gYU2gKjW9j/3tb3/Tfffdp9WrV2vYsGE1Pl8EFqd/hnm9Xnk8nkueJwIXIeKwRo0aacqUKZo8ebJCQkLUp08fFRQUaP/+/RozZky1D2vm5ORIkkpKSlRQUKCcnByFhISoU6dODswegaAm97FVq1YpOTlZTz31lK6//nodP35c0ve/TCIjI516CajDanL/Wrx4sVq1aqUOHTpI+v7j4nPnztXDDz/s1PQRCHxw3OnTp32PP/64LyEhwdewYUNfq1atfE888cRFbUvSWbeEhISanTACTk3tYzfccMM597Hk5OSanzQCRk3tX08//bSvc+fOvtDQUF9ERISve/fuvmeeecZ3+vRpB2aNQMGnZgAAgBmurAoAAMwQIgAAwAwhAgAAzBAiAADADCECAADMECIAAMAMIQIAAMwQIgAAwAwhAgAAzBAiAADADCECAADM/D+nRQrCOIEG4AAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Comparing weights\n",
    "\n",
    "W_ours = m.W  # (D, C)\n",
    "W_scik = np.vstack([s.intercept_, s.coef_.T])  # (D, C)\n",
    "\n",
    "for d in range(m.X.shape[1]):\n",
    "    plt.title(r\"$w_{cd}$, \" + f\"$d={d+1}$\")\n",
    "    plt.bar(np.arange(0, 3), W_ours[d], width=0.5, label=f\"ours\")\n",
    "    plt.bar(np.arange(0, 3) + 0.5, W_scik[d], width=0.4, label=f\"sklearn\")\n",
    "    plt.xticks(np.arange(0, 3), [\"c=1\", \"c=2\", \"c=3\"])\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bb468a3f-b015-4c48-9654-e2cabf30825d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}