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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Entropía y Ganancia de Información"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Entropía\n",
    "\n",
    "Definamos entropía para una distribución probabilista:\n",
    "\n",
    "$$H(Y) = - \\sum_{i=1}^k P(Y = y_i) log_2 P(Y = y_i)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "entropy(np.array([0.5, 0.5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08079313589591118"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "entropy(np.array([0.01, 0.99]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 6,
     "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: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1414405425418206"
      ]
     },
     "execution_count": 7,
     "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": 9,
   "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: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.16666667, 0.83333333])"
      ]
     },
     "execution_count": 10,
     "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def entropy(y):\n",
    "    p = probs(y)\n",
    "    return - np.sum(p * np.log2(p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6500224216483541"
      ]
     },
     "execution_count": 12,
     "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": 13,
   "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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si analizámos la varibale $Y$ donde la $X_1$ es $True$, tenemos: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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 $X_1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3333333333333333"
      ]
     },
     "execution_count": 16,
     "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 $X_2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4591479170272448"
      ]
     },
     "execution_count": 17,
     "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para el caso de $X_1$: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3166890883150208"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "information_gain(y_X1true, y_X1false)  # x1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para el caso de $X_2$: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.19087450462110933"
      ]
     },
     "execution_count": 20,
     "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",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "size = 200"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "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": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((100, 2), (100, 2))"
      ]
     },
     "execution_count": 25,
     "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "model = LogisticRegression()\n",
    "model.fit(X_train, y_train);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from utils import plot_decision_boundary\n",
    "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred = model.predict(X_train)\n",
    "y_test_pred = model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "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\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((100, 2), (100, 3))"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.shape, X_train2.shape  # se agregó el feature x0*x1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Grafiquemos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "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==1, 2], color=\"dodgerblue\", edgecolors='k', label=\"1\")\n",
    "plt.scatter(X_train2[y_train==-1, 1], X_train2[y_train==-1, 2], color=\"tomato\", edgecolors='k', label=\"-1\")\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "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": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred = model.predict(X_train)\n",
    "y_test_pred = model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "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": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'X[1]')"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from utils import plot_decision_boundary\n",
    "\n",
    "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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "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": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos calcular la probabilidad de cada clase:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.21, 0.79])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probs(y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "y la entropía:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7414827399312737"
      ]
     },
     "execution_count": 39,
     "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):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si utilizamos la variable $X_1$ con un umbral de $0.00$ obtenemos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "y1, y2 = split(X_train, y_train, 0, 0.00)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "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": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y1,y2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Siendo la entropía de cada uno de ellos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.0, 0.9731560354421095)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "entropy(y1), entropy(y2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.506041138429897"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cond_entropy(y1, y2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.23544160150137672"
      ]
     },
     "execution_count": 45,
     "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "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": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(-2.5, 2.5, 11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "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(f'feature={best_feature}, threshold={best_threshold}, ig={best_ig:00.2f}')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dividamos los datos de acuerdo a esta frontera:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 0.0)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_feature, best_threshold"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos ver los datos en el gráfico"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "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==1, 1], color=\"royalblue\", label=\"1\")\n",
    "plt.scatter(X_train[y_train==-1, 0], 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": 50,
   "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7414827399312737"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "entropy(y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.42"
      ]
     },
     "execution_count": 52,
     "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": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" 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 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 sk-toggleable__label-arrow\">DecisionTreeClassifier</label><div class=\"sk-toggleable__content\"><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": 53,
     "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred = clf.predict(X_train)\n",
    "y_test_pred = clf.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'X[1]')"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from utils import plot_decision_boundary\n",
    "\n",
    "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "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": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7414827399312737"
      ]
     },
     "execution_count": 58,
     "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?"
   ]
  },
  {
   "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": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}