clases/notebooks/05 Arboles de Decision.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5. Árboles de Decisión\n",
    "\n",
    "Veremos árboles de decisión y los conceptos subyacentes asociados.\n",
    "\n",
    "Haremos ejemplos de juguete y con datos generados artificialmente.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_decision_boundary(model, X, y):\n",
    "    X = X.T\n",
    "    y = y.T\n",
    "\n",
    "    # Set min and max values and give it some padding\n",
    "    x_min, x_max = X[0, :].min() - 1, X[0, :].max() + 1\n",
    "    y_min, y_max = X[1, :].min() - 1, X[1, :].max() + 1\n",
    "    h = 0.01\n",
    "\n",
    "    # Generate a grid of points with distance h between them\n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n",
    "                         np.arange(y_min, y_max, h))\n",
    "\n",
    "    # Predict the function value for the whole grid\n",
    "    Z = model(np.c_[xx.ravel(), yy.ravel()])\n",
    "    Z = Z.reshape(xx.shape)\n",
    "\n",
    "    ax = plt.gca()\n",
    "    ax.set_aspect(1)\n",
    "    # plt.axis(\"equal\")\n",
    "    # plt.contourf(xx, yy, Z, cmap=plt.cm.ocean, alpha=0.5)\n",
    "    plt.contourf(xx, yy, Z, colors=[\"red\", \"royalblue\"], alpha=0.2)\n",
    "    # plt.contourf(xx, yy, Z, cmap=plt.cm.Pastel1, alpha=0.5)\n",
    "    # plt.scatter(X[0, y==1], X[1, y==1], color=\"dodgerblue\", edgecolors='k', label=\"1\")\n",
    "    plt.scatter(X[0, y == 1], X[1, y == 1], color=\"royalblue\", label=\"1\")\n",
    "    plt.scatter(X[0, y == -1], X[1, y == -1], color=\"red\", label=\"-1\")\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Entropía y Ganancia de Información\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Entropía\n",
    "\n",
    "Definamos entropía para una distribución probabilista:\n",
    "\n",
    "$$H(Y) = - \\sum_{i=1}^k P(Y = y_i) log_2 P(Y = y_i)$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def entropy(probs):\n",
    "    return - np.sum(probs * np.log2(probs))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Veamos posibles entropías para el problema de tirar una moneda adulterada:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "entropy(np.array([0.5, 0.5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08079313589591118"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "entropy(np.array([0.01, 0.99]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.linspace(0, 1)[1:-1]\n",
    "plt.plot(X, [entropy([x, 1-x]) for x in X])\n",
    "plt.xlabel('P(Y=y_1)')\n",
    "plt.ylabel('entropy')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En el caso de dos monedas, tenemos cuatro combinaciones posibles, siendo $0.25$ la probabilidad de cada evento. Ejemplos:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "entropy(np.array([0.25, 0.25, 0.25, 0.25]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pero si las monedas estan sesgadas tendríamos:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1414405425418206"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "entropy(np.array([0.49, 0.49, 0.01, 0.01]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Entropía de un Dataset\n",
    "\n",
    "Un dataset define una distribución empírica. La entropía del dataset es entones la entropía de la distribución asociada. Definamos el cálculo de la distribución, y luego redefinamos entropía:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def probs(y):\n",
    "    _, counts = np.unique(y, return_counts=True)\n",
    "    probs = counts / counts.sum()\n",
    "    return probs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Definimos un dataset de 6 elementos con dos atributos $X_1$ y $X_2$ con dos tipos de etiquetas:\n",
    "\n",
    "$False: -1$ y $True: 1$.\n",
    "<img src=\"img/tablaDataset2.png\" width=\"100\"/>\n",
    "Siendo las etiquetas resultantes del mismo:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.array([1, 1, 1, 1, 1, -1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mediante la función \"probs\" podemos calcular la probilidad de cada clase en este dataset:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.16666667, 0.83333333])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probs(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esos resultados nos informan que hay un desbalance en el mismo (hay más probabilidad de una de las clases).\n",
    "\n",
    "Ahora obtengamos la entropía del dataset:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def entropy(y):\n",
    "    p = probs(y)\n",
    "    return - np.sum(p * np.log2(p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6500224216483541"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "entropy(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Entropía Condicional\n",
    "\n",
    "Definamos entropía condicional:\n",
    "\n",
    "$$H(Y|X) = - \\sum_{j=1}^v P(X = x_j) \\sum_{i=1}^k P(Y = y_i | X = x_j) log_2 P(Y = y_i | X = x_j)$$\n",
    "\n",
    "Equivalentemente,\n",
    "\n",
    "$$H(Y|X) = \\sum_{j=1}^v P(X = x_j) H(Y|X = x_j)$$\n",
    "\n",
    "Tomaremos $X$ binaria ($v=2$), por lo que la entropía condicional tendrá sólo dos términos.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cond_entropy(y1, y2):\n",
    "    size = y1.shape[0] + y2.shape[0]\n",
    "    return y1.shape[0] / size * entropy(y1) + y2.shape[0] / size * entropy(y2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esta función toma como argumento los dos subconjuntos de datos que se forman al considerar una de las variables como condición.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si analizámos la varibale $Y$ donde la $X_1$ es $True$, tenemos:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_X1true = np.array([1, 1, 1, 1])  # X1 = True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "de igual manera, la varibale $Y$ donde la $X_1$ es $False$, tenemos:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_X1false = np.array([1, -1])  # X1 = False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Haciendo uso de la función \"cond_entropy\" podemos obtener la entropía condicional de la variable $Y$ dado $X_1$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3333333333333333"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cond_entropy(y_X1true, y_X1false)  # x1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "De igual manera podemos calcular la entropía condicional dado la variable $X_2$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4591479170272448"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_X2true = np.array([1, 1, 1])  # X2 = True\n",
    "y_X2false = np.array([1, 1, -1])  # X2 = False\n",
    "cond_entropy(y_X2true, y_X2false)  # x2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ganancia de Información\n",
    "\n",
    "La ganancia de información será simplemente la diferencia entre entropía y entropía condicional:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def information_gain(y1, y2):\n",
    "    y = np.concatenate((y1, y2))\n",
    "    return entropy(y) - cond_entropy(y1, y2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos calcular la ganancia de información que implicaría dividir el dataset tomando como $X_1$ como nodo referencia. Para ello hacemos uso de la función \"information_gain\" que toma los dos subconjuntos de etiquetas que se formarían al tomar una u otra variable como referencia.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para el caso de $X_1$:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3166890883150208"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "information_gain(y_X1true, y_X1false)  # x1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para el caso de $X_2$:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.19087450462110933"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "information_gain(y_X2true, y_X2false)  # x2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Datos Sintéticos No Linealmente Separables\n",
    "\n",
    "Haremos algunos experimentos con datos generados sintéticamente. Estos datos serán no linealmente separables.\n",
    "\n",
    "Ejemplos típicos de datos no linealmente separables son los de tipo \"OR\", \"AND\" y \"XOR\". Usaremos datos de tipo \"OR\" para este ejemplo.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "size = 200"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(0)\n",
    "X = np.random.randn(size, 2)\n",
    "y_true = np.logical_or(X[:, 0] > 0, X[:, 1] > 0)    # datos \"OR\"\n",
    "# y_true = np.logical_xor(X[:, 0] > 0, X[:, 1] > 0)  # datos \"XOR\"\n",
    "# y_true = np.logical_and(X[:, 0] > 0, X[:, 1] > 0)  # datos \"AND\"\n",
    "y_true = y_true.astype(int)\n",
    "y_true[y_true == 0] = -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[y_true == 1, 0], X[y_true == 1, 1], color=\"royalblue\", label=\"1\")\n",
    "plt.scatter(X[y_true == -1, 0], X[y_true == -1, 1], color=\"red\", label=\"-1\")\n",
    "plt.grid()\n",
    "plt.xlabel(\"X[0]\")\n",
    "plt.ylabel(\"X[1]\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### División en Entrenamiento y Evaluación\n",
    "\n",
    "Separemos la mitad para entrenamiento y la otra para evaluación.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_size = 100\n",
    "test_size = size - train_size\n",
    "X_train, X_test = X[:train_size], X[train_size:]\n",
    "y_train, y_test = y_true[:train_size], y_true[train_size:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((100, 2), (100, 2))"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.shape, X_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Clasificación Lineal\n",
    "\n",
    "Veamos qué tan mal anda un clasificador lineal sobre estos datos.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;LogisticRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.4/modules/generated/sklearn.linear_model.LogisticRegression.html\">?<span>Documentation for LogisticRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>LogisticRegression()</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "model = LogisticRegression()\n",
    "model.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel(\"X[0]\")\n",
    "plt.ylabel(\"X[1]\")\n",
    "plot_decision_boundary(lambda x: model.predict(x), X, y_true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculemos la calidad de la predicción en entrenamiento y evaluación:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred = model.predict(X_train)\n",
    "y_test_pred = model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train accuracy: 0.91\n",
      "Test accuracy: 0.78\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "train_acc = accuracy_score(y_train, y_train_pred)\n",
    "test_acc = accuracy_score(y_test, y_test_pred)\n",
    "print(f'Train accuracy: {train_acc:0.2}')\n",
    "print(f'Test accuracy: {test_acc:0.2}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nota al Margen: Induciendo Separabilidad Lineal\n",
    "\n",
    "Muchas veces se pueden convertir datos no linealmente separables en datos separables (o casi) mediante la introducción de nuevos atributos que combinan los atributos existentes.\n",
    "Un ejemplo de estos son los atributos polinomiales.\n",
    "\n",
    "Aquí lo haremos con datos \"OR\", pero la diferencia es mucho más notable con datos de tipo \"XOR\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.pipeline import make_pipeline\n",
    "\n",
    "pre = PolynomialFeatures(\n",
    "    degree=2,\n",
    "    interaction_only=True,  # para usar solo x0*x1, no x0*x0 ni x1*x1\n",
    "    include_bias=False)\n",
    "X_train2 = pre.fit_transform(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((100, 2), (100, 3))"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.shape, X_train2.shape  # se agregó el feature x0*x1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Grafiquemos:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_train2[y_train == 1, 1], X_train2[y_train ==\n",
    "            1, 2], color=\"dodgerblue\", edgecolors='k', label=\"1\")\n",
    "plt.scatter(X_train2[y_train == -1, 1], X_train2[y_train == -\n",
    "            1, 2], color=\"tomato\", edgecolors='k', label=\"-1\")\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-2 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-2 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-2 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-2 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-2 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-2 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-2 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-2 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-2 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Pipeline(steps=[(&#x27;polynomialfeatures&#x27;,\n",
       "                 PolynomialFeatures(include_bias=False, interaction_only=True)),\n",
       "                (&#x27;logisticregression&#x27;, LogisticRegression())])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" ><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;Pipeline<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.4/modules/generated/sklearn.pipeline.Pipeline.html\">?<span>Documentation for Pipeline</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>Pipeline(steps=[(&#x27;polynomialfeatures&#x27;,\n",
       "                 PolynomialFeatures(include_bias=False, interaction_only=True)),\n",
       "                (&#x27;logisticregression&#x27;, LogisticRegression())])</pre></div> </div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" ><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;PolynomialFeatures<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.4/modules/generated/sklearn.preprocessing.PolynomialFeatures.html\">?<span>Documentation for PolynomialFeatures</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>PolynomialFeatures(include_bias=False, interaction_only=True)</pre></div> </div></div><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-4\" type=\"checkbox\" ><label for=\"sk-estimator-id-4\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;LogisticRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.4/modules/generated/sklearn.linear_model.LogisticRegression.html\">?<span>Documentation for LogisticRegression</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>LogisticRegression()</pre></div> </div></div></div></div></div></div>"
      ],
      "text/plain": [
       "Pipeline(steps=[('polynomialfeatures',\n",
       "                 PolynomialFeatures(include_bias=False, interaction_only=True)),\n",
       "                ('logisticregression', LogisticRegression())])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.pipeline import make_pipeline\n",
    "\n",
    "model = make_pipeline(\n",
    "    PolynomialFeatures(degree=2, interaction_only=True, include_bias=False),\n",
    "    LogisticRegression()\n",
    ")\n",
    "model.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred = model.predict(X_train)\n",
    "y_test_pred = model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train accuracy: 0.97\n",
      "Test accuracy: 0.86\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "train_acc = accuracy_score(y_train, y_train_pred)\n",
    "test_acc = accuracy_score(y_test, y_test_pred)\n",
    "print(f'Train accuracy: {train_acc:0.2}')\n",
    "print(f'Test accuracy: {test_acc:0.2}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'X[1]')"
      ]
     },
     "execution_count": 37,
     "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": [
    "plot_decision_boundary(lambda x: model.predict(x), X, y_true)\n",
    "plt.xlabel(\"X[0]\")\n",
    "plt.ylabel(\"X[1]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Entropía y Valores Reales\n",
    "\n",
    "Calculemos la entropía inicial, y veamos cómo condicionar la entropía sobre variables reales (i.e. no categóricas)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1, -1,\n",
       "        1,  1, -1, -1,  1, -1,  1, -1,  1, -1,  1,  1, -1, -1, -1,  1,  1,\n",
       "        1,  1,  1,  1, -1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,\n",
       "        1,  1, -1,  1,  1,  1,  1,  1,  1,  1,  1, -1,  1,  1,  1,  1,  1,\n",
       "        1,  1,  1,  1,  1,  1, -1,  1, -1, -1,  1, -1,  1,  1,  1, -1,  1,\n",
       "        1,  1,  1, -1,  1, -1, -1,  1,  1,  1,  1, -1,  1,  1,  1])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos calcular la probabilidad de cada clase:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.21, 0.79])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probs(y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "y la entropía:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7414827399312737"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "entropy(y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para hacer una división sobre una variable real usaremos un valor \"threshold\" (umbral):\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "def split(X, y, i, threshold):\n",
    "    y1 = y[X[:, i] > threshold]\n",
    "    y2 = y[X[:, i] <= threshold]\n",
    "    return y1, y2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "definimos la \"split\" que toma como argumento el dataset con sus etiquetas, el indice de la variable que usaremos para dividir el dataset y el umbral para realizarlo y nos devuelve dos subconjuntos de este dataset.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si utilizamos la variable $X_1$ con un umbral de $0.00$ obtenemos:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "y1, y2 = split(X_train, y_train, 0, 0.00)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "        1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "        1, 1, 1, 1]),\n",
       " array([ 1,  1, -1,  1, -1, -1,  1, -1,  1, -1,  1, -1,  1, -1, -1, -1,  1,\n",
       "         1, -1,  1,  1,  1,  1,  1,  1, -1,  1,  1, -1,  1,  1,  1,  1,  1,\n",
       "         1, -1,  1, -1, -1, -1,  1,  1, -1,  1, -1,  1, -1, -1,  1,  1,  1,\n",
       "        -1]))"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y1, y2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Siendo la entropía de cada uno de ellos:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.0, 0.9731560354421095)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "entropy(y1), entropy(y2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.506041138429897"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cond_entropy(y1, y2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.23544160150137672"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "information_gain(y1, y2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Buscando la Mejor División\n",
    "\n",
    "Ilustraremos un paso en la construcción del árbol de decisión.\n",
    "\n",
    "Probemos muchos threshold para ambas variables y seleccionemos la mejor división.\n",
    "\n",
    "En este caso buscaremos en una grilla uniforme de valores, pero existen técnicas mejores.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2.5, -2. , -1.5, -1. , -0.5,  0. ,  0.5,  1. ,  1.5,  2. ,  2.5])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(-2.5, 2.5, 11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i=0\tthreshold=-2.50\tig=0.00\n",
      "i=0\tthreshold=-2.00\tig=0.00\n",
      "i=0\tthreshold=-1.50\tig=0.00\n",
      "i=0\tthreshold=-1.00\tig=0.00\n",
      "i=0\tthreshold=-0.50\tig=0.12\n",
      "i=0\tthreshold=+0.00\tig=0.24\n",
      "i=0\tthreshold=+0.50\tig=0.13\n",
      "i=0\tthreshold=+1.00\tig=0.06\n",
      "i=0\tthreshold=+1.50\tig=0.03\n",
      "i=0\tthreshold=+2.00\tig=0.01\n",
      "i=0\tthreshold=+2.50\tig=0.00\n",
      "i=1\tthreshold=-2.50\tig=0.00\n",
      "i=1\tthreshold=-2.00\tig=0.02\n",
      "i=1\tthreshold=-1.50\tig=0.05\n",
      "i=1\tthreshold=-1.00\tig=0.06\n",
      "i=1\tthreshold=-0.50\tig=0.12\n",
      "i=1\tthreshold=+0.00\tig=0.32\n",
      "i=1\tthreshold=+0.50\tig=0.15\n",
      "i=1\tthreshold=+1.00\tig=0.07\n",
      "i=1\tthreshold=+1.50\tig=0.04\n",
      "i=1\tthreshold=+2.00\tig=0.00\n",
      "i=1\tthreshold=+2.50\tig=0.00\n",
      "Mejor división:\n",
      "feature=1, threshold=0.0, ig=0.32\n"
     ]
    }
   ],
   "source": [
    "best_ig = 0\n",
    "\n",
    "for i in [0, 1]:\n",
    "    for threshold in np.linspace(-2.5, 2.5, 11):\n",
    "        y1, y2 = split(X_train, y_train, i, threshold)\n",
    "        ig = information_gain(y1, y2)\n",
    "        print(f'i={i}\\tthreshold={threshold:+00.2f}\\tig={ig:.2f}')\n",
    "\n",
    "        if ig >= best_ig:\n",
    "            best_ig = ig\n",
    "            best_feature = i\n",
    "            best_threshold = threshold\n",
    "\n",
    "print('Mejor división:')\n",
    "print(\n",
    "    f'feature={best_feature}, threshold={best_threshold}, ig={best_ig:00.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dividamos los datos de acuerdo a esta frontera:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 0.0)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_feature, best_threshold"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos ver los datos en el gráfico\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_train[y_train == 1, 0], X_train[y_train ==\n",
    "            1, 1], color=\"royalblue\", label=\"1\")\n",
    "plt.scatter(X_train[y_train == -1, 0],\n",
    "            X_train[y_train == -1, 1], color=\"red\", label=\"-1\")\n",
    "\n",
    "plt.axhline(y=0, xmin=-3, xmax=3, color='green', linestyle='-.', linewidth=2)\n",
    "\n",
    "plt.xlabel(\"X[0]\")\n",
    "plt.ylabel(\"X[1]\")\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "y1, y2 = split(X_train, y_train, best_feature, best_threshold)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Con esta división, la entropía baja considerablemente:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7414827399312737"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "entropy(y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.42"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cond_entropy(y1, y2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Árbol de Decisión con Scikit-learn\n",
    "\n",
    "Aprendamos un árbol de decisión usando scikit-learn. Para ello usaremos la clase [DecisionTreeClassifier](https://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeClassifier.html):\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-3 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-3 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-3 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-3 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-3 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-3 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-3 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-3 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-3 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-3 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-3 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>DecisionTreeClassifier(criterion=&#x27;entropy&#x27;, max_depth=3, random_state=0)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-5\" type=\"checkbox\" checked><label for=\"sk-estimator-id-5\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;DecisionTreeClassifier<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.4/modules/generated/sklearn.tree.DecisionTreeClassifier.html\">?<span>Documentation for DecisionTreeClassifier</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>DecisionTreeClassifier(criterion=&#x27;entropy&#x27;, max_depth=3, random_state=0)</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "DecisionTreeClassifier(criterion='entropy', max_depth=3, random_state=0)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeClassifier\n",
    "clf = DecisionTreeClassifier(max_depth=3, criterion='entropy', random_state=0)\n",
    "clf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora predecimos y evaluamos:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred = clf.predict(X_train)\n",
    "y_test_pred = clf.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train accuracy: 1.0\n",
      "Test accuracy: 0.97\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "train_acc = accuracy_score(y_train, y_train_pred)\n",
    "test_acc = accuracy_score(y_test, y_test_pred)\n",
    "print(f'Train accuracy: {train_acc:0.2}')\n",
    "print(f'Test accuracy: {test_acc:0.2}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dibujamos la frontera de decisión:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'X[1]')"
      ]
     },
     "execution_count": 57,
     "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": [
    "plot_decision_boundary(lambda x: clf.predict(x), X_train, y_train)\n",
    "plt.xlabel(\"X[0]\")\n",
    "plt.ylabel(\"X[1]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "También podemos inspeccionar el árbol:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0.5, 0.875, 'x[1] <= -0.211\\nentropy = 0.741\\nsamples = 100\\nvalue = [21, 79]'),\n",
       " Text(0.25, 0.625, 'x[0] <= 0.069\\nentropy = 0.977\\nsamples = 34\\nvalue = [20, 14]'),\n",
       " Text(0.125, 0.375, 'entropy = 0.0\\nsamples = 20\\nvalue = [20, 0]'),\n",
       " Text(0.375, 0.375, 'entropy = 0.0\\nsamples = 14\\nvalue = [0, 14]'),\n",
       " Text(0.75, 0.625, 'x[1] <= -0.066\\nentropy = 0.113\\nsamples = 66\\nvalue = [1, 65]'),\n",
       " Text(0.625, 0.375, 'x[0] <= -0.324\\nentropy = 0.544\\nsamples = 8\\nvalue = [1, 7]'),\n",
       " Text(0.5, 0.125, 'entropy = 0.0\\nsamples = 1\\nvalue = [1, 0]'),\n",
       " Text(0.75, 0.125, 'entropy = 0.0\\nsamples = 7\\nvalue = [0, 7]'),\n",
       " Text(0.875, 0.375, 'entropy = 0.0\\nsamples = 58\\nvalue = [0, 58]')]"
      ]
     },
     "execution_count": 58,
     "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": [
    "from sklearn.tree import plot_tree\n",
    "\n",
    "plot_tree(clf, filled=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7414827399312737"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "entropy(y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejercicios\n",
    "\n",
    "1. Probar todos los experimentos con un dataset de tipo \"XOR\". ¿Qué sucede al decidir la división en el primer nivel del árbol?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Referencias\n",
    "\n",
    "Scikit-learn:\n",
    "\n",
    "- [accuracy_score](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.accuracy_score.html)\n",
    "- [User Guide: Decision Trees](https://scikit-learn.org/stable/modules/tree.html)\n",
    "- [DecisionTreeClassifier](https://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeClassifier.html)\n"
   ]
  }
 ],
 "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": "3.11.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}