05_svm.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "boxed-irish",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "postal-bracket",
   "metadata": {},
   "source": [
    "## Maquinas de vectores de soporte (*support vector machines*)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "important-germany",
   "metadata": {},
   "source": [
    "Método poderoso que se puede utilizar en clasificación (lineal y no-lineal), regresión, detección de anomalías, etc.\n",
    "\n",
    "En la figura vemos datos del conjunto \"Iris\" que son **linealmente separables**.\n",
    "\n",
    "A la izquierda hay límites de decisión de distintos modelos. Las líneas rojas separan bien los puntos, pero es muy probable que el error de generalización sea alto. La línea verde ni siquiera separa las clases.\n",
    "\n",
    "A la derecha tenemos el límite de decisión de un modelo SVM. La línea separa las clases y es lo más lejos posible de los puntos.\n",
    "\n",
    "Se puede decir que un clasificador de SVM coloca la \"calle\" más ancha posible entre las dos clases. Se llama clasificación de margen grande (*large margin classification*)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "continuing-estimate",
   "metadata": {},
   "source": [
    "![](figures_svm/fig5-1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "contrary-attraction",
   "metadata": {},
   "source": [
    "El límite de decisión está determinado (soportado) solamente por las instancias en la borde de la calle. Estas instancias son los **vectores de soporte** (*support vectors*)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "owned-possession",
   "metadata": {},
   "source": [
    "| ![](figures_svm/fig5-2.png) |\n",
    "|-----------------------------|\n",
    "| Modelos de SVM son muy sensibles al escalamiento de los *features* |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "demanding-marijuana",
   "metadata": {},
   "source": [
    "### Clasificación de margen blando (*soft margin classification*)\n",
    "\n",
    "Si no permitimos la presencia de ninguna instancia en la \"calle\", y estipulamos que todas las instancias tienen que estar en su lado correcto, tenemos **clasificación de margen duro**.\n",
    "\n",
    "Este funciona solamente si los datos son linealmente separables. Además es muy sensible a datos anómalos (*outliers*).\n",
    "\n",
    "![](figures_svm/fig5-3.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "unlikely-bracelet",
   "metadata": {},
   "source": [
    "Es preferible usar un modelo más flexible.\n",
    "\n",
    "Queremos encontrar un balance entre una \"calle\" ancha, y un límite en el número de instancias en la \"calle\" (violaciones del margen, *margin violations*).\n",
    "\n",
    "Este se llama **clasificación de margen blando**.\n",
    "\n",
    "En los modelos de SVM en Scikit-Learn se puede controlar el número de violaciones del margen con el hiperparámetro `C`.\n",
    "\n",
    "![](figures_svm/fig5-4.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "legal-respect",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.svm import LinearSVC #SVC = support vector classifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "blocked-killing",
   "metadata": {},
   "outputs": [],
   "source": [
    "iris = datasets.load_iris()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "molecular-heritage",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris[\"data\"][:, (2, 3)] #longitud pétalos, ancho pétalos\n",
    "y = (iris[\"target\"] == 2).astype(np.float64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "posted-onion",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(steps=[('scaler', StandardScaler()),\n",
       "                ('linear_svc', LinearSVC(C=1, loss='hinge'))])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svm_clf = Pipeline([\n",
    "    (\"scaler\", StandardScaler()),\n",
    "    (\"linear_svc\", LinearSVC(C=1, loss=\"hinge\")),\n",
    "])\n",
    "\n",
    "svm_clf.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "democratic-theme",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svm_clf.predict([[5.5, 1.7]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "improved-gothic",
   "metadata": {},
   "source": [
    "El clasificador de SVM **no** da información de las probabilidades de las clases (como el clasificador de regresión logística)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "analyzed-charles",
   "metadata": {},
   "source": [
    "Hay otras opciones en Scikit-Learn para obtener el mismo modelo:\n",
    "\n",
    "* `SVC(kernel=\"linear\", C=1)` pero es mucho más lento.\n",
    "* `SGDClassifier(loss=\"hinge\", alpha=1/(m*C))` a veces es útil para datos masivos.\n",
    "\n",
    "La clase `LinearSVC` regulariza el término del *bias*, así que hay que centrar los datos (restar el promedio). Este es automático con el uso de `StandardScaler`.\n",
    "\n",
    "[Notar: el modelo `SGDClassifier` que usabamos en el notebook `03_clasificación` tiene `loss='hinge'` por defecto, así que estabamos usando un SVM en un espacio de 784 dimensiones...]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ceramic-awareness",
   "metadata": {},
   "source": [
    "### Clasificación SVM no-lineal\n",
    "\n",
    "Se puede trabajar con datos no-lineales agregando más *features*, por ejemplo *features* polinomiales (como lo que vimos antes).\n",
    "\n",
    "| ![](figures_svm/fig5-5.png) |\n",
    "|-----------------------------|\n",
    "| Izquierda: datos no linealmente separables. Derecha: agregamos $x_2 = x_1^2$ para separar los datos. |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "labeled-dover",
   "metadata": {},
   "source": [
    "Ahora veremos un ejemplo con un conjunto de datos sintético que se llama **moons** (los datos tienen la forma de dos lunas crescientes)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "immune-fellowship",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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07a0DyLRP65EXH9Fd779L33/s+43cn3PNyxr0far0v/m8P3/m/6Ft2qf13OnnKvE7zCeFktchSRd3/PxGSYcH2AbQ0RNHg3aAD9PBm+poo5hiz8sKPUCi39d78o+ePDPSq/Mr9X6fvFJIKI9KWmFmbzWzRZJukbR1xjZbJX0wG+11taSXsytHAufY/NzmgUZj9TowDHMASH20UROFXo4lxeVdYoqeUNx9WtJHJT0s6YCkLe6+z8zWmNmabLPtkp6RdFDS5yStjRIskjZxfEIPvfDQQB3gRRwY6n42WjWhB0gw4GK26AlFktx9u7tf4u5vd/dPZffd5e53Zbfd3f84e/wX3f2xuBEjRYOOxuLA0Ayhl2NJcXmX2JJIKMCw2kmh3eHZz3BMDgz1NnF8Qld//mrd++S5w3U/+9hn9dQLTw38mnUe/jsoEgpqYdAO8CIODMyMT8v6Xev13f/73TNDv9tcrlu/fOvAr8mAi9lIKKiFQTvAizgwpNpRW/ZF41LQPmGQNOvvLEn7f7R/oMTPgIvuUpiHAgyt3dHd75yE0AeGFK/D0dbEi7h1njAsWrBIt73jNrlc9zx5j6ZOTWnhgoUDLX3CwIruSChotNAHhjqv01Q13cqZm57cdOZ2+3tqib/KKHmh0lLqr6CjNi3dyplTp6Zm9aVUre8jpf/5mUgoqLRQ/RUhPqR01KalWznztE53TTJV6vtItY9OIqFE0+4gHRsbbUwHaWgh54+E+JDSUZuWXhNLD/+Xwzr/VedLkn7mVT+jiT+dGKj0GaOlkPqcKRJKJE3sIA0t1PyRUB/S1GfGcxG3llD/NzFaCqnPmSKhoJJ69VccmzrW92ul/iENJfbCjHkUfdYfqp8rRkuhCn10JBRUUq/+is3Pbe7rdarwIW2Sos/6Q/VzxTgJqUIfHQkFldSrv2Lfy/v6ep0qfEibooyz/hD9XLFOQqrQR8c8FFRSr36Jfq/cV4UP6SAmjk/oli/foi/d9KXKzK8oYw5PiP6suU5CipxzlEpf3FxIKJHMdeU6lKcKH9JBdJaOqjCxstdZf4oTDut6EhICCSWSdkdoVS5fiupIefmXXmKd9Q+irichIdCHAtRMFUetcdZfD7RQgBmq2P/QVqXSUSfO+uuBFgowQ8pLW8yHUWuIiYQCdEh9aYv5UDpCTJS8gA5VX36+bqWjKpcfm4gWCpBh1nx6qlx+bCISCpCh/yEtVS8/NhEJBcjQ/zC4IhZ1rOLw56YjoQCZ1Jef7yWFK/iFLk1RfqwmEgpQcf0ezEMnoCJKU5Qfq4mEAlREt0QwyME8dGuiiNIU5cdqIqEAFdEtEfR7MA/dmiiqNBWq/JhCObBJSChovH4POqlcS3yQg3no1kTqpSmGHZeLhILG6/egk8q1xPs9mBfRmhi0NFVGUmbYcflIKGi0fg86KV1LfNdzu/o6mBfRmhi0NFVGUmbYcflIKGi0fg86KV1L/Jo3X9PXwTyVju5+kvKgLRmGHcdBQkFj9XvQ2T2xW3c/fndlryWeyjybfpLyoC2Z1Pt26oqEgsbq96Dzga98IMpBKpVEEEI/SXyY8mIqrbGmYbVhNFY/B52J4xPa/6P9s+7nINWffi71O8zKz1VMtnUQNaGY2VJJX5L0FknPSvpdd3+py3bPSjou6ZSkaXe/srwoUVf9HHTW71qvhQsWaurUlBYtWKTb3nFbpZa1T0XeJB76ypPDLoPPMvr5xC553S5ph7uvkLQj+7mXMXf/ZZIJykYHbzh5y3eh+0CGHVXGfJZ8YieUVZLuy27fJ+l98UIBuqODt3wh+0CGHerNfJb8YvehjLj7hCS5+4SZvb7Hdi7pETNzSXe7+8bSIkTj0cFbvpB9IMNehbPqV/Esk7l7sW9g9o+SuhUdPyHpPnd/Xce2L7n7ki6v8QZ3P5wlnK9L+pi77+qy3WpJqyVp2bJlV2zZsiXQb1GcyclJLV68OHYY8yLOsAaN8+iJo7rzwJ1ad+k6LV20tIDIzvX8S8/rL577izPvV/b75zHXvjx64qhu/ZdbNXX67AnBq897te5/5/254h/2+XnjTMnY2Njjg3YtFN5Ccfdf7/WYmb1gZhdmrZMLJb3Y4zUOZ99fNLOvSLpK0qyEkrVcNkrSypUrfXR0NMBvUKzx8XERZzh1j3PttrXa+8pe7Ti5QxuuL/4sedXGVee8X9nvn8dc+3LttrWSnXufm+eOf9jn542zLmL3oWyV9KHs9ockfXXmBmb2GjN7bfu2pOsl7S0tQiARZdfyJ45P6KEXHjrzfnuO7KlcX8Kw5UrKnf2J3YfyPyVtMbMPS3pe0s1Sq8Ql6fPufoOkEUlfMTOpFe/97v5QpHiBWcoaUlp2LX/m+/3eg79Xub6EYftimM/Sn6gtFHc/6u7XuvuK7Pux7P7DWTKRuz/j7r+UfV3m7p+KGTMwUxlDSsseutx+v2mfPvN++360j6HTmFPskhdQaWWVocoeutzt/WZi6DRmIqEAQyhr9eFetfz79txXSBLr9n4z0ZeAmWL3oQCVFXp5kLl0q+Wv3bZWdz9+dyF9Ge33a8LIJIRDCwUYUMwZ9MzeRopIKMCAYg4prcvVCMu4FDDKQ8kLGFCsIaVlltqK1jlCLvUhyJgfLRSgYuqyWCVlu/ohoQAVU5fZ23Up2+EsSl5AxdRh9nadynY4ixYKgNLVpWyHc5FQAJSuLmU7nIuSF4DS1aFsh9looQAAgiChAACCIKEAAIIgoQAAgiChAACCIKEAAIIgoQAAgiChAACCIKEAAIIgoQAAgiChAACCIKEAAIIgoQAAgiChAACCIKEAAIIgoQAAgiChAACCIKEAAIIgoQAAgiChAACCIKEAAIIgoQAAgiChAACCiJpQzOxmM9tnZqfN7Mo5tnuPmf3AzA6a2e1lxggAyCd2C2WvpBsl7eq1gZktkLRB0nslXSrp/WZ2aTnhAQDyelXMN3f3A5JkZnNtdpWkg+7+TLbtFyWtkrS/8AABALlFTSg5XSTphx0/H5L0zm4bmtlqSauzH0+Y2d6CYwvhAkk/jh1EDsQZFnGGU4UYperEuXLQJxaeUMzsHyUt7/LQJ9z9q3leost93m1Dd98oaWP2vo+5e89+mVQQZ1jEGVYV4qxCjFK14hz0uYUnFHf/9SFf4pCkizt+fqOkw0O+JgAgsNid8nk8KmmFmb3VzBZJukXS1sgxAQBmiD1s+HfM7JCkd0naZmYPZ/e/wcy2S5K7T0v6qKSHJR2QtMXd9+V4+Y0FhR0acYZFnGFVIc4qxCg1IE5z79odAQBAX6pQ8gIAVAAJBQAQRG0SSh/LuDxrZt8zs93DDI8bVFWWmzGzpWb2dTP71+z7kh7bRdmf8+0fa/l09vhTZnZ5WbH1EeOomb2c7bvdZvbJsmPM4thkZi/2mreVwr7M4pgvzuj708wuNrOdZnYg+5z/5y7bRN+fOePsf3+6ey2+JP2CWhNyxiVdOcd2z0q6IOU4JS2Q9G+S3iZpkaQ9ki4tOc7/Len27Pbtkv5XKvszz/6RdIOkr6k1j+lqSd9NMMZRSf8Q63+xI47/JOlySXt7PB51X/YRZ/T9KelCSZdnt18r6enU/jf7iLPv/VmbFoq7H3D3H8SOYz454zyz3Iy7T0lqLzdTplWS7stu3yfpfSW//1zy7J9VkjZ7y3ckvc7MLkwsxiS4+y5Jx+bYJPa+lJQrzujcfcLdn8huH1drZOpFMzaLvj9zxtm32iSUPrikR8zs8WyplhR1W25m6D92n0bcfUJq/fNJen2P7WLszzz7J/Y+zPv+7zKzPWb2NTO7rJzQ+hZ7X/Yjmf1pZm+R9A5J353xUFL7c444pT73ZxXW8jrDhl/GRZL+o7sfNrPXS/q6mX0/O/MJJkCcuZebGcZccfbxMoXvzy7y7J9S9uEc8rz/E5Le7O6TZnaDpL+XtKLowAYQe1/mlcz+NLPFkr4s6ePu/srMh7s8Jcr+nCfOvvdnpRKKD7+Mi9z9cPb9RTP7ilqliaAHwABxlrLczFxxmtkLZnahu09kzfEXe7xG4fuzizz7J/aSPfO+f+cH2N23m9nfmtkF7p7aAoKx92UuqexPM1uo1kH679z9wS6bJLE/54tzkP3ZqJKXmb3GzF7bvi3perWuyZKaFJab2SrpQ9ntD0ma1bKKuD/z7J+tkj6Yjai5WtLL7RJeSeaN0cyWm7Wu3WBmV6n1eTxaYox5xd6XuaSwP7P3v0fSAXf/yx6bRd+feeIcaH+WPbqgqC9Jv6NW5j8h6QVJD2f3v0HS9uz229QabbNH0j61SlDJxelnR4I8rdZIoRhx/rykHZL+Nfu+NKX92W3/SFojaU1229S6MNu/Sfqe5hj5FzHGj2b7bY+k70h6d9kxZnE8IGlC0snsf/PDqe3LnHFG35+SflWt8tVTknZnXzektj9zxtn3/mTpFQBAEI0qeQEAikNCAQAEQUIBAARBQgEABEFCAQAEQUIBAARBQgFKkC0Vfl12+8/N7NOxYwJCq9TSK0CFrZN0Z7bm2Tsk/XbkeIDgmNgIlMTMviFpsaRRdz9uZm9TayHO/+DuN8WNDhgeJS+gBGb2i2pd1OiEt64/IW9dK+XDcSMDwiGhAAXLVmv+O7UurPQTM/uNyCEBhSChAAUys5+V9KCkP3X3A5LWS/rvUYMCCkIfChCJmf28pE9Juk7S5939f0QOCRgKCQUAEAQlLwBAECQUAEAQJBQAQBAkFABAECQUAEAQJBQAQBAkFABAECQUAEAQJBQAQBD/HxjbA/XHiJgIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "X, y = make_moons(n_samples=100, noise=0.15, random_state=42)\n",
    "\n",
    "def plot_dataset(X, y, axes):\n",
    "    plot(X[:, 0][y==0], X[:, 1][y==0], \"bs\")\n",
    "    plot(X[:, 0][y==1], X[:, 1][y==1], \"g^\")\n",
    "    axis(axes)\n",
    "    grid(True, which='both')\n",
    "    xlabel(\"$x_1$\")\n",
    "    ylabel(\"$x_2$\")\n",
    "    \n",
    "plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "varied-backing",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/graeme/anaconda3/lib/python3.7/site-packages/sklearn/svm/_base.py:977: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
      "  \"the number of iterations.\", ConvergenceWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Pipeline(steps=[('poly_features', PolynomialFeatures(degree=3)),\n",
       "                ('scaler', StandardScaler()),\n",
       "                ('svm_clf', LinearSVC(C=10, loss='hinge'))])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.svm import LinearSVC\n",
    "\n",
    "polynomial_svm_clf = Pipeline([\n",
    "    (\"poly_features\", PolynomialFeatures(degree=3)),\n",
    "    (\"scaler\", StandardScaler()),\n",
    "    (\"svm_clf\", LinearSVC(C=10, loss=\"hinge\"))\n",
    "])\n",
    "\n",
    "polynomial_svm_clf.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "central-factory",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_predictions(clf, axes):\n",
    "    x0s = linspace(axes[0], axes[1], 100)\n",
    "    x1s = linspace(axes[2], axes[3], 100)\n",
    "    x0, x1 = meshgrid(x0s, x1s)\n",
    "    X = c_[x0.ravel(), x1.ravel()]\n",
    "    y_pred = clf.predict(X).reshape(x0.shape)\n",
    "    y_decision = clf.decision_function(X).reshape(x0.shape)\n",
    "    contourf(x0, x1, y_pred, cmap=cm.brg, alpha=0.2)\n",
    "    contourf(x0, x1, y_decision, cmap=cm.brg, alpha=0.1)\n",
    "    \n",
    "plot_predictions(polynomial_svm_clf, [-1.5, 2.5, -1, 1.5])\n",
    "plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "italic-correlation",
   "metadata": {},
   "source": [
    "#### Núcleo polinomial (*polynomial kernel*)\n",
    "\n",
    "Usar un polinomio de grado bajo, como lo que hicimos arriba, no funciona bien para datos complejos. Usar un polinomio de grado alto crea un número grande de *features* y el modelo es lento.\n",
    "\n",
    "Hay un truco que se llama el **truco del núcleo** (*kernel trick*) que da el mismo resultado que antes, sin la necesidad de agregar más *features* a los datos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "animal-protocol",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(steps=[('scaler', StandardScaler()),\n",
       "                ('svm_clf', SVC(C=5, coef0=1, kernel='poly'))])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.svm import SVC\n",
    "poly_kernel_svm_clf = Pipeline([\n",
    "    (\"scaler\", StandardScaler()),\n",
    "    (\"svm_clf\", SVC(kernel=\"poly\", degree=3, coef0=1, C=5))\n",
    "])\n",
    "\n",
    "poly_kernel_svm_clf.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "continental-article",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(steps=[('scaler', StandardScaler()),\n",
       "                ('svm_clf', SVC(C=5, coef0=100, degree=10, kernel='poly'))])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly10_kernel_svm_clf = Pipeline([\n",
    "    (\"scaler\", StandardScaler()),\n",
    "    (\"svm_clf\", SVC(kernel=\"poly\", degree=10, coef0=100, C=5))\n",
    "])\n",
    "\n",
    "poly10_kernel_svm_clf.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "overhead-europe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 756x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = subplots(ncols=2, figsize=(10.5, 4), sharey=True)\n",
    "\n",
    "sca(axes[0])\n",
    "plot_predictions(poly_kernel_svm_clf, [-1.5, 2.45, -1, 1.5])\n",
    "plot_dataset(X, y, [-1.5, 2.45, -1, 1.5])\n",
    "title(\"$d=3, r=1, C=5$\")\n",
    "\n",
    "sca(axes[1])\n",
    "plot_predictions(poly100_kernel_svm_clf, [-1.5, 2.45, -1, 1.5])\n",
    "plot_dataset(X, y, [-1.5, 2.45, -1, 1.5])\n",
    "title(\"$d=10, r=100, C=5$\")\n",
    "ylabel(\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "stock-design",
   "metadata": {},
   "source": [
    "* Izquierda: clasificador de SVM con *kernel* de polinomio de grado 3.\n",
    "* Derecha: con *kernel* de polinomio de grado 10.\n",
    "\n",
    "El hiperparámetro `coef0` controla la importancia de los polinomios de grado alto versus los polinomios de grado bajo. Es un parámetro del *kernel* (más información abajo)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "marine-norway",
   "metadata": {},
   "source": [
    "#### Agregando *features* de similitud (*similarity features*)\n",
    "\n",
    "Otra técnica para datos no-lineales es el uso de más *features* calculados con una **función de similitud**.\n",
    "\n",
    "Esta función mide la similitud entre una instancia y algún punto de referencia."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "stylish-correlation",
   "metadata": {},
   "source": [
    "Como ejemplo, volvemos a los datos unidimensionales. Agregamos un par de puntos de referencia en $x_1 = -2$ y $x_1 = 1$.\n",
    "\n",
    "Definimos la función de similitud como $$\\phi_{\\gamma}(\\boldsymbol{x},\\mathscr{l}) = \\exp \\left( -\\gamma || \\boldsymbol{x} - \\mathscr{l} ||^2 \\right)$$\n",
    "\n",
    "Esta función se llama la **función de base radial gaussiana** (*Gaussian RBF*)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "medium-denial",
   "metadata": {},
   "source": [
    "| ![](figures_svm/fig5-8.png) |\n",
    "|-----------------------------|\n",
    "| Gaussian RBF con $\\gamma=0.3$ |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sacred-identity",
   "metadata": {},
   "source": [
    "Como ejemplo, elegimos $\\gamma = 0.3$. consideramos la instancia $x_1 = -1$. Tiene una distancia de $1$ del primer punto de referencia, y $2$ del segundo punto.\n",
    "\n",
    "Entonces los nuevos *features* son $x_2 = \\exp(-0.3 \\times 1^2) \\approx 0.74$ y $x_3 = \\exp(-0.3 \\times 2^2) \\approx 0.30$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "close-distinction",
   "metadata": {},
   "source": [
    "En la figura arriba, a la derecha, vemos los nuevos *features* (sin el original). Los datos ahora son linealmente separables.\n",
    "\n",
    "El uso de *similarity features* es algo que se puede aplicar a cualquier algoritmo de *machine learning* (como es el caso con *features* polinomiales).\n",
    "\n",
    "Se puede implementar la función RBF gaussiana en un SVM usando el truco del *kernel* de nuevo (para no generar muchos *features* nuevos)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "rolled-midwest",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 756x504 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.svm import SVC\n",
    "\n",
    "gamma1, gamma2 = 0.1, 5\n",
    "C1, C2 = 0.001, 1000\n",
    "hyperparams = (gamma1, C1), (gamma1, C2), (gamma2, C1), (gamma2, C2)\n",
    "\n",
    "svm_clfs = []\n",
    "for gamma, C in hyperparams:\n",
    "    rbf_kernel_svm_clf = Pipeline([\n",
    "            (\"scaler\", StandardScaler()),\n",
    "            (\"svm_clf\", SVC(kernel=\"rbf\", gamma=gamma, C=C))\n",
    "        ])\n",
    "    rbf_kernel_svm_clf.fit(X, y)\n",
    "    svm_clfs.append(rbf_kernel_svm_clf)\n",
    "\n",
    "fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(10.5, 7), sharex=True, sharey=True)\n",
    "\n",
    "for i, svm_clf in enumerate(svm_clfs):\n",
    "    plt.sca(axes[i // 2, i % 2])\n",
    "    plot_predictions(svm_clf, [-1.5, 2.45, -1, 1.5])\n",
    "    plot_dataset(X, y, [-1.5, 2.45, -1, 1.5])\n",
    "    gamma, C = hyperparams[i]\n",
    "    plt.title(r\"$\\gamma = {}, C = {}$\".format(gamma, C), fontsize=16)\n",
    "    if i in (0, 1):\n",
    "        plt.xlabel(\"\")\n",
    "    if i in (1, 3):\n",
    "        plt.ylabel(\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "level-confidentiality",
   "metadata": {},
   "source": [
    "* Un $\\gamma$ mayor reduce el ancho de la curva gaussiana, reduciendo la influencia de cada instancia $\\rightarrow$ el límite de decisión será más irregular y adaptado a las posiciones de las instancias (riesgo de *overfitting*!)\n",
    "* Un $\\gamma$ menor tiene el efecto opuesto.\n",
    "\n",
    "$\\gamma$ actua como un parámetro de regularización (similar al parámetro `C`)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "polyphonic-poultry",
   "metadata": {},
   "source": [
    "Hay otros *kernels* (menos usados), por ejemplo *string kernels* usados en clasificación de textos o secuencias de ADN."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "exempt-mouse",
   "metadata": {},
   "source": [
    "#### Complejidad computacional\n",
    "\n",
    "La clase `LinearSVC` está basada en la librería `liblinear` que implementa un algoritmo optimizado para SVMs lineales ([paper](https://www.csie.ntu.edu.tw/~cjlin/papers/cddual.pdf)).\n",
    "\n",
    "Este algoritmo no permite el truco del *kernel* pero escala linealmente con el número de instancias de entrenamiento y *features*: $\\mathcal{O}(m \\times n)$.\n",
    "\n",
    "Se puede aumentar la precisión con el hiperparámetro $\\epsilon$ (llamado `tol` en Scikit-Learn)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "wrapped-public",
   "metadata": {},
   "source": [
    "La clase `SVC` está basada en la librería `libsvm` que implementa un algoritmo que funciona con el truco del *kernel* ([wikipedia](https://en.wikipedia.org/wiki/Sequential_minimal_optimization)).\n",
    "\n",
    "El tiempo de entrenamiento escala entre $\\mathcal{O}(m^2 \\times n)$ y $\\mathcal{O}(m^3 \\times n)$.\n",
    "\n",
    "Por lo tanto, es muy lento con muchas instancias de entrenamiento."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "respected-thompson",
   "metadata": {},
   "source": [
    "![](figures_svm/table5-1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "owned-sociology",
   "metadata": {},
   "source": [
    "### Regresión SVM\n",
    "\n",
    "Se puede invertir la meta del algoritmo: ajustar la \"calle\" para tener la mayoría de las instancias en la \"calle\" y limitar violaciones de margen (instancias fuera de la \"calle\").\n",
    "\n",
    "El ancho de la calle está controlado por $\\epsilon$.\n",
    "\n",
    "![](figures_svm/fig5-10.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "domestic-silicon",
   "metadata": {},
   "source": [
    "Agregando más instancias dentro del margen no afecta las predicciones del modelo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "finished-lawyer",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearSVR(epsilon=1.5, random_state=42)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "m = 50\n",
    "X = 2 * np.random.rand(m, 1)\n",
    "y = (4 + 3 * X + np.random.randn(m, 1)).ravel()\n",
    "\n",
    "\n",
    "from sklearn.svm import LinearSVR\n",
    "\n",
    "svm_reg = LinearSVR(epsilon=1.5, random_state=42)\n",
    "svm_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "gorgeous-relief",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 2.0, 3.0, 11.0)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "axes = [0,2,3,11]\n",
    "x1s = np.linspace(axes[0], axes[1], 100).reshape(100, 1)\n",
    "y_pred = svm_reg.predict(x1s)\n",
    "plot(x1s, y_pred, \"k-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "plot(x1s, y_pred + svm_reg.epsilon, \"k--\")\n",
    "plot(x1s, y_pred - svm_reg.epsilon, \"k--\")\n",
    "plot(X, y, \"bo\")\n",
    "xlabel(r\"$x_1$\", fontsize=18)\n",
    "legend(loc=\"upper left\", fontsize=18)\n",
    "axis(axes)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "regulation-sentence",
   "metadata": {},
   "source": [
    "Para regresión no-lineal se puede usar un *kernel* de nuevo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "selective-juice",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "m = 100\n",
    "X = 2 * np.random.rand(m, 1) - 1\n",
    "y = (0.2 + 0.1 * X + 0.5 * X**2 + np.random.randn(m, 1)/10).ravel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "settled-repair",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVR(C=100, degree=2, kernel='poly')"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.svm import SVR\n",
    "\n",
    "svm_poly_reg = SVR(kernel=\"poly\", degree=2, C=100, epsilon=0.1, gamma=\"scale\")\n",
    "svm_poly_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "settled-daniel",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.0, 1.0, 0.0, 1.0)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "axes = [-1,1,0,1]\n",
    "x1s = np.linspace(axes[0], axes[1], 100).reshape(100, 1)\n",
    "y_pred = svm_poly_reg.predict(x1s)\n",
    "plot(x1s, y_pred, \"k-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "plot(x1s, y_pred + svm_poly_reg.epsilon, \"k--\")\n",
    "plot(x1s, y_pred - svm_poly_reg.epsilon, \"k--\")\n",
    "plot(X, y, \"bo\")\n",
    "xlabel(r\"$x_1$\", fontsize=18)\n",
    "legend(loc=\"upper left\", fontsize=18)\n",
    "axis(axes)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "regular-moisture",
   "metadata": {},
   "source": [
    "| ![](figures_svm/fig5-11.png) |\n",
    "|------------------------------|\n",
    "| Ejemplo del libro. Hay más regularización en el gráfico a la derecha. |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "planned-bangladesh",
   "metadata": {},
   "source": [
    "## Los detalles del método\n",
    "\n",
    "* El término del *bias* es $b$.\n",
    "* El vector de pesos de los *features* es $\\boldsymbol{w}$ (antes usabamos $\\boldsymbol{\\theta}$).\n",
    "* Ahora **no** hay un *feature* $x_0 = 1$ que corresponde al *bias*."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "liked-genome",
   "metadata": {},
   "source": [
    "### Función de decisión y predicciones\n",
    "\n",
    "La función de decisión del modelo es\n",
    "\n",
    "$$h = \\boldsymbol{w}^T \\boldsymbol{x} + b$$\n",
    "\n",
    "El clasificador de SVM lineal predice la clase de una instancia en la siguiente manera:\n",
    "\n",
    "$$\\hat{y} = \\begin{cases} 0 & \\boldsymbol{w}^T \\boldsymbol{x} + b < 0 \\\\ 1 & \\boldsymbol{w}^T \\boldsymbol{x} + b \\geq 0 \\end{cases}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "existing-knife",
   "metadata": {},
   "source": [
    "Volvemos al ejemplo de los datos de \"Iris\"\n",
    "\n",
    "![](figures_svm/fig5-4-half.png)\n",
    "\n",
    "![](figures_svm/fig5-12.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "defensive-lingerie",
   "metadata": {},
   "source": [
    "En este caso la función de decisión corresponde a un plano bidimensional (hay 2 *features*).\n",
    "\n",
    "El límite de decisión es la intersección entre el plano de datos y el plano definido por $h$.\n",
    "\n",
    "El margen está definido por las líneas donde $h = \\pm 1$.\n",
    "\n",
    "Entrenamiento de un modelo SVM lineal: encontrar los valores de $\\boldsymbol{w}$ y $b$ tal que el margen sea lo más ancho posible, sin violaciones (margen duro) o con pocas violaciones (margen blando).\n",
    "\n",
    "##### Más features\n",
    "\n",
    "Con $n$ *features*, la función de decisión define un hiperplano de $n$ dimensiones, y el límite de decisión es un hiperplano de $(n-1)$ dimensiones."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "turned-angel",
   "metadata": {},
   "source": [
    "### Objetivo del entrenamiento\n",
    "\n",
    "La pendiente del plano definido por la función de decisión está dada por $||\\boldsymbol{w}||$.\n",
    "\n",
    "Si dividimos la pendiente por $2$, el margen será más ancho.\n",
    "\n",
    "| ![](figures_svm/fig5-13.png) |\n",
    "|------------------------------|\n",
    "| Ejemplo con solamente $1$ *feature* |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "extra-patrick",
   "metadata": {},
   "source": [
    "Queremos minimizar $||\\boldsymbol{w}||$ para obtener un margen amplio.\n",
    "\n",
    "Pero si aplicamos un margen duro, queremos evitar cualquier violación del margen. Entonces necesitamos\n",
    "\n",
    "$$h(\\boldsymbol{x}_i) \\begin{cases} > 1 & y^{(i)} = 1 \\\\ < -1 & y^{(i)} = 0 \\end{cases}$$\n",
    "\n",
    "Primero, definimos:\n",
    "\n",
    "$$t^{(i)} = \\begin{cases} +1 & y^{(i)} = 1 \\\\ -1 & y^{(i)} = 0 \\end{cases}$$\n",
    "\n",
    "Ahora podemos expresar nuestra restricción como\n",
    "\n",
    "$$t^{(i)}(\\boldsymbol{w}^T \\boldsymbol{x}^{(i)} + b) \\geq 1$$\n",
    "\n",
    "para todas las instancias."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "african-series",
   "metadata": {},
   "source": [
    "##### Entrenamiento con margen duro\n",
    "\n",
    "Por lo tanto, el entrenamiento del clasificador SVM lineal (margen duro) corresponde al siguiente problema de **optimización restringida**:\n",
    "\n",
    "$$\\underset{\\boldsymbol{w},b}{\\text{minimizar}} \\;\\; \\frac{1}{2}\\boldsymbol{w}^T\\boldsymbol{w} \\;\\; \\text{sujeto a} \\;\\; t^{(i)}(\\boldsymbol{w}^T \\boldsymbol{x}^{(i)} + b) \\geq 1 \\;\\; \\text{para} \\; i=1,\\ldots,m$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "catholic-anaheim",
   "metadata": {},
   "source": [
    "Usamos $\\frac{1}{2}\\boldsymbol{w}^T\\boldsymbol{w} = \\frac{1}{2}||\\boldsymbol{w}||^2$ en vez de $||\\boldsymbol{w}||$ porque es diferenciable en $\\boldsymbol{w} = 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "congressional-marsh",
   "metadata": {},
   "source": [
    "##### Entrenamiento con margen blando\n",
    "\n",
    "En el caso de un margen blando, introducimos una variable \"floja\" (*slack variable*) para cada instancia.\n",
    "\n",
    "$\\zeta^{(i)}$ es una medida de la violación del margen permitida para la instancia $i$.\n",
    "\n",
    "Ahora tenemos dos objetivos en conflicto: reducir $\\zeta^{(i)}$ para reducir violaciones del margen, y reducir $\\frac{1}{2}\\boldsymbol{w}^T\\boldsymbol{w}$ para aumentar el margen.\n",
    "\n",
    "Con el hiperparámetro $C$ se puede definir la importancia relativa de estos dos objetivos."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "absolute-circumstances",
   "metadata": {},
   "source": [
    "$$\\underset{\\boldsymbol{w},b,\\zeta}{\\text{minimizar}} \\;\\; \\frac{1}{2}\\boldsymbol{w}^T\\boldsymbol{w} + C\\sum_{i=1}^m \\zeta^{(i)} \\;\\; \\text{sujeto a} \\;\\; t^{(i)}(\\boldsymbol{w}^T \\boldsymbol{x}^{(i)} + b) \\geq 1 - \\zeta^{(i)} \\; y \\; \\zeta^{(i)} \\geq 0 \\; \\text{para} \\; i=1,\\ldots,m$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "awful-handle",
   "metadata": {},
   "source": [
    "#### Optimización cuadrática (*quadratic programming*)\n",
    "\n",
    "Los problemas de optimización del margen duro y blando son problemas **convexos cuadráticos con restricciones lineales**.\n",
    "\n",
    "Tales problemas se llaman problemas de optimización cuadrática (*quadratic programming*, QP).\n",
    "\n",
    "Hay muchos métodos disponibles para resolver problemas así. La formulación general del problema es:\n",
    "\n",
    "$$\\underset{\\boldsymbol{p}}{\\text{minimizar}} \\;\\; \\frac{1}{2}\\boldsymbol{p}^T \\boldsymbol{H} \\boldsymbol{p} + \\boldsymbol{f}^T\\boldsymbol{p} \\;\\; \\text{sujeto a} \\;\\; \\boldsymbol{A}\\boldsymbol{p} \\leq \\boldsymbol{b}$$\n",
    "\n",
    "donde:\n",
    "\n",
    "* $\\boldsymbol{p}$ es un vector de dimensión $n_p$.\n",
    "* $\\boldsymbol{H}$ es una matriz de dimensión $n_p \\times n_p$.\n",
    "* $\\boldsymbol{f}$ es un vector de dimensión $n_p$.\n",
    "* $\\boldsymbol{A}$ es una matriz de dimensión $n_c \\times n_p$ ($n_c = $ número de restricciones)\n",
    "* $\\boldsymbol{b}$ es un vector de dimensión $n_c$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "level-incentive",
   "metadata": {},
   "source": [
    "La expresión $\\boldsymbol{A}\\boldsymbol{p} \\leq \\boldsymbol{b}$ define $n_c$ restricciones.\n",
    "\n",
    "Se puede traducir esta formulación del problema a lo que vimos para el clasificador SVM lineal con margen duro:\n",
    "\n",
    "* $n_p = n + 1$, donde $n$ es el número de *features* ($+1$ para el *bias*).\n",
    "* $n_c = m$, donde $m$ es el número de instancias de entrenamiento.\n",
    "* $\\boldsymbol{H}$ es la matriz de identidad con $0$ en el elemento $(0,0)$ (para eliminar el término del *bias*).\n",
    "* $\\boldsymbol{f} = \\boldsymbol{0}$\n",
    "* $\\boldsymbol{b} = \\boldsymbol{-1}$\n",
    "* $\\boldsymbol{a}^{(i)} = -t^{(i)} \\dot{\\boldsymbol{x}}^{(i)}$ donde $\\dot{\\boldsymbol{x}}^{(i)}$ es igual a $\\boldsymbol{x}^{(i)}$ aparte del elemento $\\dot{\\boldsymbol{x}}_0 = 1$ (*bias*) y $\\boldsymbol{a}^{(i)}$ es la $i$-esima fila de la matriz $\\boldsymbol{A}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acute-hybrid",
   "metadata": {},
   "source": [
    "Así que se puede entrenar un clasificador de SVM (margen duro) con algún algoritmo para resolver el problema QP.\n",
    "\n",
    "El vector resultante $\\boldsymbol{p}$ contendrá el término del *bias* $b = p_0$ y los pesos de los *features* $w_i = p_i$ para $i = 1,\\ldots,n$.\n",
    "\n",
    "Se puede usar un *solver* de QP para el problema de margen blando."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "careful-requirement",
   "metadata": {},
   "source": [
    "### El problema dual\n",
    "\n",
    "Dado un problema de optimización restringida (**problema primario**) se puede expresar un problema diferente pero relacionado que se llama el **problema dual**.\n",
    "\n",
    "La solución al problema dual típicamente da un límite inferior a la solución del problema primario. \n",
    "\n",
    "En algunos casos especiales (función de objetivo es convexa, las restricciones son continuamente diferenciable y convexas) las soluciones de los problemas primario y dual coinciden.\n",
    "\n",
    "SVM satisface estas condiciones, así que podemos trabajar con el problema dual:\n",
    "\n",
    "$$\\underset{\\alpha}{\\text{minimizar}} \\;\\; \\frac{1}{2}\\sum_{i=1}^m \\sum_{j=1}^m \\alpha^{(i)} \\alpha^{(j)} t^{(i)} t^{(j)} \\boldsymbol{x}^{(i)T} \\boldsymbol{x}^{(j)} - \\sum_{i=1}^m \\alpha^{(i)} \\;\\; \\text{sujeto a} \\;\\; \\alpha^{(i)} \\geq 0 \\;\\; \\text{para} \\;\\; i = 1,\\ldots,m$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "deluxe-indication",
   "metadata": {},
   "source": [
    "Una vez que hemos encontrado el vector $\\hat{\\alpha}$ que minimiza esta ecuación (con un *solver* de QP) podemos calcular $\\hat{\\boldsymbol{w}}$ y $\\hat{b}$ que minimizan el problema primal:\n",
    "\n",
    "$$\\hat{\\boldsymbol{w}} = \\sum_{i=1}^m \\hat{\\alpha}^{(i)} t^{(i)} \\boldsymbol{x}^{(i)}$$\n",
    "\n",
    "$$\\hat{b} = \\frac{1}{n_s} \\sum_{i=1}^m \\left( t^{(i)} - \\hat{\\boldsymbol{w}}^T \\boldsymbol{x}^{(i)} \\right)$$\n",
    "\n",
    "Es más rápido resolver el problema dual cuando hay menos instancias de entrenamiento que *features*, es decir $m < n$.\n",
    "\n",
    "Más importante, el problema dual permite el truco del *kernel* (*kernel trick*)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "legislative-testimony",
   "metadata": {},
   "source": [
    "### SVM con *kernels*\n",
    "\n",
    "Ejemplo: aplicar un polinomio de grado 2 a datos de entrenamiento bidimensionales para entrenar un clasificador SVM lineal en los datos transformados:\n",
    "\n",
    "$$\\phi(\\boldsymbol{x}) = \\phi \\left( \\begin{pmatrix} x_1 \\\\ x_2 \\end{pmatrix} \\right) = \\begin{pmatrix} x_1^2 \\\\ \\sqrt{2}x_1x_2 \\\\ x_2^2 \\end{pmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "protected-hampton",
   "metadata": {},
   "source": [
    "¿Que pasa con el producto punto de los vectores transformados?\n",
    "\n",
    "$$\\begin{split} \\phi(\\boldsymbol{a})^T\\phi(\\boldsymbol{b}) &= \\begin{pmatrix} a_1^2 \\\\ \\sqrt{2}a_1a_2 \\\\ a_2^2 \\end{pmatrix} \\begin{pmatrix} b_1^2 \\\\ \\sqrt{2}b_1b_2 \\\\ b_2^2 \\end{pmatrix}  = a_1^2b_1^2 + 2a_1b_1a_2b_2 + a_2^2b_2^2 \\\\ &= (a_1b_1 + a_2b_2)^2 = \\left( \\begin{pmatrix} a_1 \\\\ a_2 \\end{pmatrix}^T \\begin{pmatrix} b_1 \\\\ b_2 \\end{pmatrix} \\right)^2 = \\left( \\boldsymbol{a}^T \\boldsymbol{b} \\right)^2 \\end{split}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "harmful-count",
   "metadata": {},
   "source": [
    "Aplicando la transformación $\\phi$ a todas las instancias, tendremos, en el problema dual, el producto punto $\\phi(\\boldsymbol{x}^{(i)})^T\\phi(\\boldsymbol{x}^{(j)})$.\n",
    "\n",
    "Pero ahora sabemos que (en el caso del polinomio de grado 2) podemos reemplazar ese producto punto por $\\left( x^{(i)T}x^{(j)} \\right)^2$.\n",
    "\n",
    "Así que, no hace falta aplicar la transformación $\\phi$.\n",
    "\n",
    "Esta es la esencia del truco del *kernel*: es mucho más eficiente computacionalmente."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "informed-contents",
   "metadata": {},
   "source": [
    "La función $K(\\boldsymbol{a},\\boldsymbol{b}) = (\\boldsymbol{a}^T \\boldsymbol{b})^2$ se llama un *kernel* polinomial de grado 2.\n",
    "\n",
    "Un *kernel* (en este contexto) es una función capaz de calcular el producto punto $\\phi(\\boldsymbol{a})^T \\phi(\\boldsymbol{b})$ usando solamente los vectores originales $\\boldsymbol{a}$ y $\\boldsymbol{b}$, sin saber nada de $\\phi$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "amateur-singer",
   "metadata": {},
   "source": [
    "*Kernels* comunes:\n",
    "\n",
    "* Lineal: $K(\\boldsymbol{a},\\boldsymbol{b}) = \\boldsymbol{a}^T \\boldsymbol{b}$\n",
    "* Polinomial: $K(\\boldsymbol{a},\\boldsymbol{b}) = \\left( \\gamma \\boldsymbol{a}^T \\boldsymbol{b} + r \\right)^d$\n",
    "* RBF gaussiana: $K(\\boldsymbol{a},\\boldsymbol{b}) =\\exp \\left( -\\gamma || \\boldsymbol{a} - \\boldsymbol{b} ||^2 \\right)$\n",
    "* Sigmoide: $K(\\boldsymbol{a},\\boldsymbol{b}) = \\tanh \\left( \\gamma \\boldsymbol{a}^T \\boldsymbol{b} + r \\right)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "accepting-respondent",
   "metadata": {},
   "source": [
    "### Teorema de Mercer\n",
    "\n",
    "Si una función $K(\\boldsymbol{a},\\boldsymbol{b})$ respeta algunas condiciones llamadas **condiciones de Mercer** (continua, simetrica en sus argumentos, etc.) entonces existe una función $\\phi$ que mapea los vectores $\\boldsymbol{a}$ y $\\boldsymbol{b}$ a otro espacio tal que $K(\\boldsymbol{a},\\boldsymbol{b}) = \\phi(\\boldsymbol{a})^T \\phi(\\boldsymbol{b})$.\n",
    "\n",
    "En el caso del *kernel* RBF gaussiana, $\\phi$ corresponde a un mapeo a un espacio de dimensión infinita..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "integrated-accident",
   "metadata": {},
   "source": [
    "##### Predicciones usando kernels\n",
    "\n",
    "Usando un *kernel* quizás no podemos obtener $\\hat{\\boldsymbol{w}}$. Entonces, ¿cómo podemos realizar predicciones con el modelo?\n",
    "\n",
    "$$\\begin{split} h_{\\hat{\\boldsymbol{w}},\\hat{b}} \\left( \\phi \\left( \\boldsymbol{x}^{(n)} \\right) \\right) &= \\hat{\\boldsymbol{w}}^T \\phi(\\boldsymbol{x}^{(n)}) + \\hat{b} = \\left( \\sum_{i=1}^m \\hat{\\alpha}^{(i)} t^{(i)} \\phi(\\boldsymbol{x}^{(i)} \\right) \\phi(\\boldsymbol{x}^{(n)}) + \\hat{b} \\\\ &= \\sum_{i=1}^m \\hat{\\alpha}^{(i)}t^{(i)} \\left( \\phi(\\boldsymbol{x}^{(i)})^T \\phi(\\boldsymbol{x}^{(n)}) \\right) + \\hat{b} \\\\ &= \\underset{\\hat{\\alpha}^{(i)} > 0}{\\sum_{i=1}^m} \\hat{\\alpha}^{(i)}t^{(i)}K(\\boldsymbol{x}^{(i)},\\boldsymbol{x}^{(n)}) + \\hat{b} \\end{split}$$\n",
    "\n",
    "Notar que $\\alpha^{(i)} \\neq 0$ solamente para los vectores de soporte, así que las predicciones requiere el producto punto entre el vector de la nueva instancia $\\boldsymbol{x}^{(n)}$ y los vectores de soporte.\n",
    "\n",
    "El término del *bias* se puede conseguir por el mismo truco:\n",
    "\n",
    "$$\\begin{split} \\hat{b} &= \\frac{1}{n_s} \\sum_{i=1}^m (t^{(i)} - \\hat{\\boldsymbol{w}}^T \\phi(\\boldsymbol{x}^{(i)})) = \\frac{1}{n_s} \\sum_{i=1}^m \\left( t^{(i)} - \\left( \\sum_{j=1}^m \\hat{\\alpha}^{(j)}t^{(j)}\\phi(\\boldsymbol{x}^{(j)}) \\right)^T \\phi(\\boldsymbol{x}^{(i)}) \\right) \\\\ &= \\frac{1}{n_s} \\sum_{i=1}^m \\left( t^{(i)} - \\sum_{j=1}^m \\hat{\\alpha}^{(j)}t^{(j)}K(\\boldsymbol{x}^{(i)},\\boldsymbol{x}^{(j)}) \\right) \\end{split}$$\n",
    "\n",
    "donde todas las sumas incluyen solamente valores del índice $i$ donde $\\hat{\\alpha}^{(i)} > 0$ (es decir, los vectores de soporte)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "structured-effectiveness",
   "metadata": {},
   "source": [
    "#### Online SVMs\n",
    "\n",
    "Ahora veremos brevemente como se puede entrenar un clasificador de SVM en forma *online* (incremental).\n",
    "\n",
    "Para SVM lineal, una opción es descenso por gradiente (con `SGDClassifier` por ejemplo) para minimizar la función de costo abajo (derivado del problema primario):\n",
    "\n",
    "$$J(\\boldsymbol{w},b) = \\frac{1}{2}\\boldsymbol{w}^T\\boldsymbol{w} + C\\sum_{i=1}^m \\max \\left( 0, 1-t^{(i)}(\\boldsymbol{w}^T \\boldsymbol{x}^{(i)} + b) \\right)$$\n",
    "\n",
    "* La primera suma empuje el modelo hacia un vector $\\boldsymbol{w}$ pequeño (margen más amplio).\n",
    "* La segunda suma calcula el total de todas las violaciones del margen. El valor para cada instancia es proporcional a la distancia entre la instancia y el lado correcto de la \"calle\"."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "structured-bicycle",
   "metadata": {},
   "source": [
    "##### Hinge Loss\n",
    "\n",
    "La función $\\max(0,1-t)$ se llama la función de *hinge loss*. No es diferenciable en $t=1$, pero se puede usar una **subderivada** en $t=1$ (cualquier valor entre $-1$ y $0$).\n",
    "\n",
    "![](figures_svm/hinge_loss.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fancy-utilization",
   "metadata": {},
   "source": [
    "##### Online SVM con kernel\n",
    "\n",
    "También es posible entrenar un modelo de SVM con kernel en forma incremental:\n",
    "\n",
    "[Incremental and Decremental SVM Learning](https://proceedings.neurips.cc/paper/2000/file/155fa09596c7e18e50b58eb7e0c6ccb4-Paper.pdf)\n",
    "\n",
    "[Fast Kernel Classifiers with Online and Active Learning](https://www.jmlr.org/papers/volume6/bordes05a/bordes05a.pdf)\n",
    "\n",
    "Estos métodos están implementados en C++ y Matlab. Si hay muchos datos, podría ser mejor considerar una red neuronal."
   ]
  }
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