07_ensambles_random_forests.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "drawn-peripheral",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "technological-highland",
   "metadata": {},
   "source": [
    "## Ensamble de modelos y *random forest*\n",
    "\n",
    "En un ensamble de modelos combinamos varios modelos para mejorar las predicciones (clasificación o regresión) de los modelos individuales.\n",
    "\n",
    "Un grupo de modelos así se llama un **ensamble de modelos** y la técnica se llama *ensemble learning*.\n",
    "\n",
    "Por ejemplo:\n",
    "\n",
    "* Se puede entrenar un grupo de árboles de decisión, cada uno en un subconjunto aleatorio del conjunto de entrenamiento.\n",
    "* Para realizar predicciones, obtenemos las predicciones de cada árbol y la predicción final es la clase que obtiene la mayoría de los votos.\n",
    "* Este ensamble de modelos se llama un *random forest*.\n",
    "* Aunque es un método simple, es uno de los algoritmos más poderosos de *machine learning*."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "alive-constitutional",
   "metadata": {},
   "source": [
    "### Clasificadores con votos\n",
    "\n",
    "| ![](figures_ensamble/fig7-1.png) |\n",
    "|----------------------------------|\n",
    "| Un grupo de clasificadores diversos. |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "compressed-stroke",
   "metadata": {},
   "source": [
    "| ![](figures_ensamble/fig7-2.png) |\n",
    "|----------------------------------|\n",
    "| Clasificador por votos (*hard voting*) |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "proper-translator",
   "metadata": {},
   "source": [
    "Un clasificador por votos a veces logra un *accuracy* mayor que el mejor clasificador del ensamble!\n",
    "\n",
    "De hecho, incluso si cada clasificador es **débil** (es solo ligeramente mejor que adivinanzas al azar), el ensamble puede ser un clasificador **fuerte** (si hay muchos clasificadores y son muy diversos).\n",
    "\n",
    "Por ejemplo: $1000$ clasificadores que son correctos 51% del tiempo. Usando la clase votado por la mayoría se puede esperar un rendimiento de 75%.\n",
    "\n",
    "Este es verdad sólo si todos los clasificadores son independientes, y cometen errores sin correlaciones. Pero ya que están entrenados usando los mismos datos habrán correlaciones. Así que el rendimiento será un poco menor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "hungarian-charlotte",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.datasets import make_moons\n",
    "\n",
    "X, y = make_moons(n_samples=500, noise=0.30, random_state=42)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "sporting-industry",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.ensemble import VotingClassifier\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.svm import SVC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "statutory-mapping",
   "metadata": {},
   "outputs": [],
   "source": [
    "log_clf = LogisticRegression()\n",
    "rnd_clf = RandomForestClassifier()\n",
    "svm_clf = SVC()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "brown-indonesia",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "VotingClassifier(estimators=[('lr', LogisticRegression()),\n",
       "                             ('rf', RandomForestClassifier()), ('svc', SVC())])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "voting_clf = VotingClassifier(estimators=[('lr', log_clf), \n",
    "                                          ('rf', rnd_clf), ('svc', svm_clf)],\n",
    "                              voting='hard')\n",
    "voting_clf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "cooked-darwin",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LogisticRegression 0.864\n",
      "RandomForestClassifier 0.896\n",
      "SVC 0.896\n",
      "VotingClassifier 0.912\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "for clf in (log_clf, rnd_clf, svm_clf, voting_clf):\n",
    "    clf.fit(X_train, y_train)\n",
    "    y_pred = clf.predict(X_test)\n",
    "    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "understood-provider",
   "metadata": {},
   "source": [
    "Si los clasificadores pueden dar la probabilidad para las clases (tienen un método `predict_proba()`) se puede predecir la clase con la mayor probabilidad, promediada sobre los clasificadores individuales. Este se llama *soft voting*.\n",
    "\n",
    "Para implementar este, hay que usar `voting='soft'` en `VotingClassifier`, y todos los clasificadores tienen que tener un método de `predict_proba()`.\n",
    "\n",
    "Por defecto SVC no tiene `predict_proba()`, pero se puede elegir la opción `True` para el hiperparámetro `probability` de ese modelo.\n",
    "\n",
    "**Ejercicio**: implementar *soft voting* en el modelo arriba."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "western-joining",
   "metadata": {},
   "source": [
    "### *Bagging* y *pasting*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "minor-poison",
   "metadata": {},
   "source": [
    "Otro método de tener un grupo de diverso de predictores es usar el mismo algoritmo para cada clasificador, pero usando distintos subconjuntos de entrenamiento.\n",
    "\n",
    "* Si reemplazamos las instancias en el conjunto total cada vez que está elegida para un subconjunto (es decir, la misma instancia puede aparecer varias veces en el subconjunto) se llama *bagging* (*bootstrap aggregating*).\n",
    "* Si **no** reemplazamos (cada instancia aparece solamente una vez en el subconjunto) se llama *pasting*.\n",
    "\n",
    "![](figures_ensamble/fig7-4.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "classical-guard",
   "metadata": {},
   "source": [
    "Con todos los predictores entrenados, agregamos las predicciones para llegar a la predicción del ensamble para una nueva instancia.\n",
    "\n",
    "* Para clasificación la función de agregación es típicamente el **modo estadístico** (la predicción más frecuente).\n",
    "* Para regresión es típicamente el promedio.\n",
    "\n",
    "Ya que usamos subconjuntos de entrenamiento, el *bias* es mayor para cada predictor individual, pero la agregación reduce el *bias* y la varianza.\n",
    "\n",
    "Es muy fácil parallelizar la operación de un ensamble."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fourth-slovakia",
   "metadata": {},
   "source": [
    "##### Bagging/pasting en Scikit-Learn\n",
    "\n",
    "En Scikit-Learn se puede usar *bagging/pasting* muy facilmente. El código abajo es para entrenar 500 clasificadores de árbol de decisión, con 100 instancias elegidas aleatoriamente del conjunto de entrenamiento para cada árbol.\n",
    "\n",
    "La elección de las instancias es con reemplazo (*bagging*). Se puede cambiar a *pasting* con `bootstrap=False`.\n",
    "\n",
    "También se puede usar un valor entre $0.0$ y $1.0$ para `max_samples`, y multiplicará el número total de instancias de entrenamiento por ese valor.\n",
    "\n",
    "`n_jobs` es el número de núcleos (*cores*) de CPU usado. El valor `-1` indica que queremos usar todos los *cores* disponibles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "suspended-pound",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.ensemble import BaggingClassifier\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "\n",
    "bag_clf = BaggingClassifier(DecisionTreeClassifier(), n_estimators=500,\n",
    "                            max_samples=100, bootstrap=True, n_jobs=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "lesser-promotion",
   "metadata": {},
   "outputs": [],
   "source": [
    "bag_clf.fit(X_train, y_train)\n",
    "y_pred = bag_clf.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "coordinated-preservation",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.904\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "print(accuracy_score(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "framed-leather",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.896\n"
     ]
    }
   ],
   "source": [
    "tree_clf = DecisionTreeClassifier(random_state=42,max_depth=5)\n",
    "tree_clf.fit(X_train, y_train)\n",
    "y_pred_tree = tree_clf.predict(X_test)\n",
    "print(accuracy_score(y_test, y_pred_tree))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "stone-doctor",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree_clf.get_depth()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "residential-corner",
   "metadata": {},
   "source": [
    "`BaggingClassifier` implementa *soft voting* automaticamente si el clasificador de base puede estimar probabilidades de las clases (tiene el método `predict_proba()`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "protecting-compensation",
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.colors import ListedColormap\n",
    "\n",
    "def plot_decision_boundary(clf, X, y, axes=[-1.5, 2.45, -1, 1.5], alpha=0.5, contour=True):\n",
    "    x1s = np.linspace(axes[0], axes[1], 100)\n",
    "    x2s = np.linspace(axes[2], axes[3], 100)\n",
    "    x1, x2 = np.meshgrid(x1s, x2s)\n",
    "    X_new = np.c_[x1.ravel(), x2.ravel()]\n",
    "    y_pred = clf.predict(X_new).reshape(x1.shape)\n",
    "    custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
    "    plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)\n",
    "    if contour:\n",
    "        custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])\n",
    "        plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)\n",
    "    plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\", alpha=alpha)\n",
    "    plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\", alpha=alpha)\n",
    "    plt.axis(axes)\n",
    "    plt.xlabel(r\"$x_1$\", fontsize=18)\n",
    "    plt.ylabel(r\"$x_2$\", fontsize=18, rotation=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "alive-newcastle",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(ncols=2, figsize=(14,6), sharey=True)\n",
    "plt.sca(axes[0])\n",
    "plot_decision_boundary(tree_clf, X, y)\n",
    "plt.title(\"Decision Tree\", fontsize=14)\n",
    "plt.sca(axes[1])\n",
    "plot_decision_boundary(bag_clf, X, y)\n",
    "plt.title(\"Decision Trees with Bagging\", fontsize=14)\n",
    "plt.ylabel(\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "stone-collect",
   "metadata": {},
   "source": [
    "El ensamble tiene un *bias* similar al árbol individual, pero hay menos varianza (comete el mismo número de errores en los datos de entrenamiento, pero el límite de decisión es menos irregular)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "amended-error",
   "metadata": {},
   "source": [
    "##### Evaluación *out-of-bag*\n",
    "\n",
    "Con *bagging* es posible tener la misma instancia usada varias veces en el entrenamiento de un predictor, mientras para otro no está usada ni una vez.\n",
    "\n",
    "![](figures_ensamble/fig_wiki_oob.jpg)\n",
    "\n",
    "Por defect, `BaggingClassifier` toma $m$ instancias del conjunto de entrenamiento, con reemplazo (`bootstrap=True`), donde $m$ es el tamaño del conjunto.\n",
    "\n",
    "$\\sim 63$% de las instancias están usadas, en promedio, para cada predictor. Los demás $37$% se llaman instancias *out-of-bag* (oob).\n",
    "\n",
    "Cada predictor tendrá un conjunto de instancias \"oob\" diferente.\n",
    "\n",
    "Podemos usar las instancias \"oob\" para evaluación del modelo, en vez de usar un conjunto de validación, con `oob_score=True`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "integral-sharing",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BaggingClassifier(base_estimator=DecisionTreeClassifier(), n_estimators=500,\n",
       "                  n_jobs=-1, oob_score=True)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bag_clf = BaggingClassifier(DecisionTreeClassifier(), n_estimators=500,\n",
    "                            bootstrap=True, n_jobs=-1, oob_score=True)\n",
    "\n",
    "bag_clf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "horizontal-filing",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9013333333333333"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bag_clf.oob_score_"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "convenient-portuguese",
   "metadata": {},
   "source": [
    "Esperamos un *accuracy* de 90.1% en el conjunto de preuba..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "purple-palmer",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.896"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "y_pred = bag_clf.predict(X_test)\n",
    "accuracy_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "intelligent-clarity",
   "metadata": {},
   "source": [
    "También se puede obtener la función de decisión \"oob\" para cada instancia de entrenamiento.\n",
    "\n",
    "En este caso el clasificador de base (`DecisionTreeClassifier`) tiene un método `predict_proba()`, así que la función de decisión retorna las probabilidades de cada clase para cada instancia de entrenamiento."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "outdoor-competition",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "       [0.07920792, 0.92079208],\n",
       "       [0.203125  , 0.796875  ],\n",
       "       [1.        , 0.        ],\n",
       "       [0.9787234 , 0.0212766 ],\n",
       "       [0.12571429, 0.87428571],\n",
       "       [0.98404255, 0.01595745],\n",
       "       [0.        , 1.        ],\n",
       "       [0.01030928, 0.98969072],\n",
       "       [1.        , 0.        ],\n",
       "       [0.95505618, 0.04494382],\n",
       "       [0.29032258, 0.70967742],\n",
       "       [0.98412698, 0.01587302],\n",
       "       [1.        , 0.        ],\n",
       "       [0.        , 1.        ],\n",
       "       [0.99      , 0.01      ],\n",
       "       [0.        , 1.        ],\n",
       "       [0.04639175, 0.95360825],\n",
       "       [0.98979592, 0.01020408],\n",
       "       [1.        , 0.        ],\n",
       "       [0.02259887, 0.97740113],\n",
       "       [0.65517241, 0.34482759]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bag_clf.oob_decision_function_"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "humanitarian-breeding",
   "metadata": {},
   "source": [
    "##### Parches aleatorios y sub-espacios aleatorios (random patches, random subspaces)\n",
    "\n",
    "Se puede elegir los *features* usados en un `BaggingClassifier` aleatoriamente también. Hay dos hiperparámetros:\n",
    "\n",
    "* `max_features`\n",
    "* `bootstrap_features`\n",
    "\n",
    "Estos son equivalentes a `max_samples` y `bootstrap` pero para los *features* en vez de las instancias.\n",
    "\n",
    "Entonces, cada predictor está entrenado con un subconjunto aleatorio diferente de los *features*. Este es útil cuando los datos tienen muchas dimensiones.\n",
    "\n",
    "* Parches aleatorios (*random patches*) corresponde a usar *bagging* para instancias y *features*\n",
    "* Subespacios aleatorios (*random subspaces*) corresponde a usar todas las instancias de entrenamiento pero aplicar *bagging* a los *features* (`bootstrap=False`, `max_samples=1.0`, `bootstrap_features=True`, `max_features=x` donde `x < 1.0`)\n",
    "\n",
    "Usando subconjuntos de *features* tenemos aún más diversidad de predictores, así que el *bias* aumenta y la varianza disminuye."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "noticed-arthur",
   "metadata": {},
   "source": [
    "### Random Forests\n",
    "\n",
    "Ya hemos usado un *random forest* (ensamble de árboles de decisión, usualmente ocupando *bagging* con `max_samples` igual al tamaño del conjunto de entrenamiento).\n",
    "\n",
    "En vez de usar `BaggingClassifier` tenemos `RandomForestClassifier` que es más optimizado (también hay `RandomForestRegressor` para regresión)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "regional-texas",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.ensemble import RandomForestClassifier\n",
    "\n",
    "rnd_clf = RandomForestClassifier(n_estimators=500, max_leaf_nodes=16, n_jobs=-1)\n",
    "rnd_clf.fit(X_train, y_train)\n",
    "\n",
    "y_pred_rf = rnd_clf.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "adopted-fellowship",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1,\n",
       "       0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0,\n",
       "       0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0,\n",
       "       0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0,\n",
       "       1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1,\n",
       "       1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred_rf"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "certain-saskatchewan",
   "metadata": {},
   "source": [
    "En un *random forest* un nodo está dividido en cada árbol usando el mejor *feature* en un conjunto aleatorio de *features*.\n",
    "\n",
    "Así que un *random forest* tiene más aleatoriedad que un árbol de decisión individual $\\Rightarrow$ más *bias*, menos varianza."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "posted-african",
   "metadata": {},
   "source": [
    "#### Extra-Trees\n",
    "\n",
    "Se puede usar umbrales aleatorios para cada *feature* en la división de los nodos, en vez de usar el mejor umbral posible (como lo que pasa con un árbol de decisión normal).\n",
    "\n",
    "Un *random forest* así se llama un ensamble de *extremely randomized trees* (*Extra-Trees*).\n",
    "\n",
    "En Scikit-Learn está disponible con `ExtraTreesClassifier`.\n",
    "\n",
    "Este modelo de nuevo aumenta el *bias* pero reduce la varianza."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "basic-worcester",
   "metadata": {},
   "source": [
    "#### Importancia de los *features*\n",
    "\n",
    "Con un *random forest* se puede determinar la importancia relativa de cada *feature*.\n",
    "\n",
    "La importancia de un *feature* está dada por cuanto está reducido la **impureza** (en promedio, sobre todos los árboles del bosque) por nodos que utilizan ese *feature*.\n",
    "\n",
    "El promedio es un promedio ponderado, donde el peso de cada nodo es igual al número de instancias de entrenamiento asociado.\n",
    "\n",
    "Scikit-Learn calcula esta importancia automaticamente para cada *feature* después del entrenamiento, y normaliza los resultados tal que $\\sum_{i=0}^{n} I_i = 1$, donde $I_i$ es la importancia de *feature* $i$.\n",
    "\n",
    "Se puede acceder a esta información con la variable `feature_importances_`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "identical-victoria",
   "metadata": {},
   "source": [
    "##### Ejemplo con los dígitos de MNIST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "foster-fisher",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import fetch_openml\n",
    "\n",
    "mnist = fetch_openml('mnist_784', version=1, as_frame=False)\n",
    "mnist.target = mnist.target.astype(np.uint8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "electoral-swiss",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestClassifier(random_state=42)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rnd_clf = RandomForestClassifier(n_estimators=100, random_state=42)\n",
    "rnd_clf.fit(mnist[\"data\"], mnist[\"target\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "artistic-christianity",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_digit(data):\n",
    "    image = data.reshape(28, 28)\n",
    "    plt.imshow(image, cmap = mpl.cm.hot,\n",
    "               interpolation=\"nearest\")\n",
    "    plt.axis(\"off\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "checked-astrology",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(1, 0.0, 'No importante'),\n",
       " Text(1, 0.009791489757332336, 'Muy importante')]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_digit(rnd_clf.feature_importances_)\n",
    "\n",
    "cbar = plt.colorbar(ticks=[rnd_clf.feature_importances_.min(), rnd_clf.feature_importances_.max()])\n",
    "cbar.ax.set_yticklabels(['No importante', 'Muy importante'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "combined-breast",
   "metadata": {},
   "source": [
    "### Boosting\n",
    "\n",
    "*Boosting* se refiere a cualquier método de ensamble que combina varios modelos débiles en un modelo fuerte.\n",
    "\n",
    "La idea general es entrenar los modelos secuencialmente, cada modelo intentando a \"corregir\" los errores del modelo anterior.\n",
    "\n",
    "Dos métodos más populares:\n",
    "* *AdaBoost* (*Adaptive Boosting*)\n",
    "* *Gradient Boosting*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "variable-recipient",
   "metadata": {},
   "source": [
    "### AdaBoost\n",
    "\n",
    "Ejemplo de clasificación:\n",
    "\n",
    "1. El primer clasificador está entrenado y realiza predicciones (clasificaciones) en los datos de entrenamiento.\n",
    "2. Los pesos de las instancias mal clasificadas están aumentados.\n",
    "3. El segundo clasificador está entrenado usando los datos con los nuevos pesos, realiza predicciones.\n",
    "4. Los pesos de las instancias mal clasificadas están aumentados de nuevo, etc...\n",
    "\n",
    "![](figures_ensamble/fig7-7.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "therapeutic-seven",
   "metadata": {},
   "source": [
    "Como ejemplo, abajo vemos los límites de decisión de $5$ predictores consecutivos en el conjunto de *moons* (cada predictor es un clasificador de SVM con mucha regularización y un kernel de RBF).\n",
    "\n",
    "El primer clasificador comete muchos errores, los pesos de estas instancias están *boosted*, el segundo clasificador es mejor, etc...\n",
    "\n",
    "| ![](figures_ensamble/fig7-8.png) |\n",
    "|----------------------------------|\n",
    "| Dos secuencias de *AdaBoost*. En la figura a la derecha las instancias mal clasificadas tienen la mitad del peso aplicado a la izquierda. |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "essential-influence",
   "metadata": {},
   "source": [
    "Una vez que todos los predictores estén entrenados, el ensamble realiza predicciones en una manera similar a *bagging* o *pasting*, pero los predictores tienen pesos distintos según su precisión en los datos ponderados de entrenamiento.\n",
    "\n",
    "Una desvantaja importante: no se puede paralelizar el método, ya que cada predictor requiere el resultado del predictor anterior."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "violent-polish",
   "metadata": {},
   "source": [
    "#### En mas detalles...\n",
    "\n",
    "Definimos un vector de pesos para todas las instancias de entrenamiento $w^{(i)}$.\n",
    "\n",
    "Inicializamos estos pesos a $1/m$, donde $m$ es el número de instancias.\n",
    "\n",
    "Calculamos la taza ponderada de error del $j$-esima predictor así:\n",
    "\n",
    "$$r_j = \\frac{1}{\\sum_{i=1}^m w^{(i)}} \\left( \\underset{\\hat{y}^{(i)}_j \\neq y^{(i)}}{\\sum_{i=1}^m w^{(i)}} \\right)$$\n",
    "\n",
    "donde $\\hat{y}^{(i)}_j$ es la predicción del $j$-esima predictor para la $i$-esima instancia.\n",
    "\n",
    "El peso del predictor $\\alpha_j$ está dado por:\n",
    "\n",
    "$$\\alpha_j = \\eta \\log \\frac{1-r_j}{r_j}$$\n",
    "\n",
    "donde $\\eta$ es la taza de aprendizaje (por defect igual a $1$) para el proceso de *boosting*. (Hay similitudes con descenso por gradiente...)\n",
    "\n",
    "Si los predicciones del predictor son aleatorios, $\\alpha_j \\approx 0$, si son siempre incorrectos (peor que aleatorio) $\\alpha_j < 0$.\n",
    "\n",
    "Ahora, los pesos de las instancias están actualizados:\n",
    "\n",
    "$$w^{(i)} = \\begin{cases} w^{(i)} & \\hat{y}^{(i)}_j = y^{(i)} \\\\ w^{(i)} \\exp(\\alpha_j) & \\hat{y}^{(i)}_j \\neq y^{(i)} \\end{cases}$$\n",
    "\n",
    "Después, todos los pesos de las instancias están normalizados (dividido por $\\sum_{i=1}^m w^{(i)}$).\n",
    "\n",
    "Finalmente, un nuevo predictor está entrenado con los nuevos valores de $w^{(i)}$, calculamos $\\alpha$ para el nuevo predictor, actualizamos los valores de $w^{(i)}$ y repetimos el proceso.\n",
    "\n",
    "Para realizar predicciones, *AdaBoost* calcula las predicciones de todos los predictores y aplica los pesos $\\alpha_j$. La clase predicha es la que recibe la mayoría de votos ponderados:\n",
    "\n",
    "$$\\hat{y}(\\boldsymbol{x}) = \\underset{k}{\\text{argmax}} \\underset{\\hat{y}_j(\\boldsymbol{x}) = k}{\\sum_{j=1}^N} \\alpha_j$$\n",
    "\n",
    "donde $N$ es el número de predictores."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "simplified-standard",
   "metadata": {},
   "source": [
    "Scikit-Learn ocupa una versión multiclase de *AdaBoost* que se llama *SAMME* (*Stagewise Additive Modeling using a Multiclass Exponential loss function*).\n",
    "\n",
    "Con dos clases, SAMME es equivalente a *AdaBoost*.\n",
    "\n",
    "Si los predictores pueden estimar probabilidades para las clases (tienen el método `predict_proba()`) Scikit-Learn puede ocupar una variante de SAMME que se llama *SAMME.R* que utiliza estas probabilidades y típicamente funciona mejor."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "attached-laugh",
   "metadata": {},
   "source": [
    "En el ejemplo abajo usamos un tocón de decisión (*decision stump*, un árbol de decisión con `max_depth=1`: un nodo de decisión y dos nodos de hoja)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "atmospheric-omega",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AdaBoostClassifier(base_estimator=DecisionTreeClassifier(max_depth=1),\n",
       "                   learning_rate=0.5, n_estimators=200)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.ensemble import AdaBoostClassifier\n",
    "\n",
    "ada_clf = AdaBoostClassifier(DecisionTreeClassifier(max_depth=1),\n",
    "                             n_estimators=200,\n",
    "                             algorithm=\"SAMME.R\",\n",
    "                             learning_rate=0.5)\n",
    "\n",
    "ada_clf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "satisfied-finnish",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_decision_boundary(ada_clf, X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "expanded-bowling",
   "metadata": {},
   "source": [
    "### Gradient Boosting\n",
    "\n",
    "En este método la idea es ajustar el nuevo predictor a los errores residuos cometidos por el predictor anterior.\n",
    "\n",
    "Como ejemplo, consideramos regresión con árboles de decisión."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "radical-construction",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Datos cuadráticos\n",
    "\n",
    "np.random.seed(42)\n",
    "X = np.random.rand(100, 1) - 0.5\n",
    "y = 3*X[:, 0]**2 + 0.05 * np.random.randn(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "grateful-imagination",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeRegressor(max_depth=2)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "tree_reg1 = DecisionTreeRegressor(max_depth=2)\n",
    "tree_reg1.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "passing-finish",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeRegressor(max_depth=2)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y2 = y - tree_reg1.predict(X)\n",
    "\n",
    "tree_reg2 = DecisionTreeRegressor(max_depth=2)\n",
    "tree_reg2.fit(X, y2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "capable-geneva",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeRegressor(max_depth=2)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y3 = y2 - tree_reg2.predict(X)\n",
    "\n",
    "tree_reg3 = DecisionTreeRegressor(max_depth=2)\n",
    "tree_reg3.fit(X, y3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "equipped-carolina",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_23407/1684835290.py:2: DeprecationWarning: Calling np.sum(generator) is deprecated, and in the future will give a different result. Use np.sum(np.fromiter(generator)) or the python sum builtin instead.\n",
      "  y_pred = np.sum(tree.predict(X_new) for tree in (tree_reg1, tree_reg2, tree_reg3))\n"
     ]
    }
   ],
   "source": [
    "X_new = np.array([[0.8]])\n",
    "y_pred = np.sum(tree.predict(X_new) for tree in (tree_reg1, tree_reg2, tree_reg3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "alpha-convenience",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.75026781])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "accepted-choir",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_predictions(regressors, X, y, axes, label=None, style=\"r-\", data_style=\"b.\", data_label=None):\n",
    "    x1 = np.linspace(axes[0], axes[1], 500)\n",
    "    y_pred = sum(regressor.predict(x1.reshape(-1, 1)) for regressor in regressors)\n",
    "    plt.plot(X[:, 0], y, data_style, label=data_label)\n",
    "    plt.plot(x1, y_pred, style, linewidth=2, label=label)\n",
    "    if label or data_label:\n",
    "        plt.legend(loc=\"upper center\", fontsize=16)\n",
    "    plt.axis(axes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "chinese-dinner",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_23407/3820871828.py:3: DeprecationWarning: Calling np.sum(generator) is deprecated, and in the future will give a different result. Use np.sum(np.fromiter(generator)) or the python sum builtin instead.\n",
      "  y_pred = sum(regressor.predict(x1.reshape(-1, 1)) for regressor in regressors)\n",
      "/tmp/ipykernel_23407/3820871828.py:3: DeprecationWarning: Calling np.sum(generator) is deprecated, and in the future will give a different result. Use np.sum(np.fromiter(generator)) or the python sum builtin instead.\n",
      "  y_pred = sum(regressor.predict(x1.reshape(-1, 1)) for regressor in regressors)\n",
      "/tmp/ipykernel_23407/3820871828.py:3: DeprecationWarning: Calling np.sum(generator) is deprecated, and in the future will give a different result. Use np.sum(np.fromiter(generator)) or the python sum builtin instead.\n",
      "  y_pred = sum(regressor.predict(x1.reshape(-1, 1)) for regressor in regressors)\n",
      "/tmp/ipykernel_23407/3820871828.py:3: DeprecationWarning: Calling np.sum(generator) is deprecated, and in the future will give a different result. Use np.sum(np.fromiter(generator)) or the python sum builtin instead.\n",
      "  y_pred = sum(regressor.predict(x1.reshape(-1, 1)) for regressor in regressors)\n",
      "/tmp/ipykernel_23407/3820871828.py:3: DeprecationWarning: Calling np.sum(generator) is deprecated, and in the future will give a different result. Use np.sum(np.fromiter(generator)) or the python sum builtin instead.\n",
      "  y_pred = sum(regressor.predict(x1.reshape(-1, 1)) for regressor in regressors)\n",
      "/tmp/ipykernel_23407/3820871828.py:3: DeprecationWarning: Calling np.sum(generator) is deprecated, and in the future will give a different result. Use np.sum(np.fromiter(generator)) or the python sum builtin instead.\n",
      "  y_pred = sum(regressor.predict(x1.reshape(-1, 1)) for regressor in regressors)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$y$')"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 792x792 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(11,11))\n",
    "\n",
    "plt.subplot(321)\n",
    "plot_predictions([tree_reg1], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"$h_1(x_1)$\", style=\"g-\", data_label=\"Training set\")\n",
    "plt.ylabel(\"$y$\", fontsize=16, rotation=0)\n",
    "plt.title(\"Residuals and tree predictions\", fontsize=16)\n",
    "\n",
    "plt.subplot(322)\n",
    "plot_predictions([tree_reg1], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"$h(x_1) = h_1(x_1)$\", data_label=\"Training set\")\n",
    "plt.ylabel(\"$y$\", fontsize=16, rotation=0)\n",
    "plt.title(\"Ensemble predictions\", fontsize=16)\n",
    "\n",
    "plt.subplot(323)\n",
    "plot_predictions([tree_reg2], X, y2, axes=[-0.5, 0.5, -0.5, 0.5], label=\"$h_2(x_1)$\", style=\"g-\", data_style=\"k+\", data_label=\"Residuals\")\n",
    "plt.ylabel(\"$y - h_1(x_1)$\", fontsize=16)\n",
    "\n",
    "plt.subplot(324)\n",
    "plot_predictions([tree_reg1, tree_reg2], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"$h(x_1) = h_1(x_1) + h_2(x_1)$\")\n",
    "plt.ylabel(\"$y$\", fontsize=16, rotation=0)\n",
    "\n",
    "plt.subplot(325)\n",
    "plot_predictions([tree_reg3], X, y3, axes=[-0.5, 0.5, -0.5, 0.5], label=\"$h_3(x_1)$\", style=\"g-\", data_style=\"k+\")\n",
    "plt.ylabel(\"$y - h_1(x_1) - h_2(x_1)$\", fontsize=16)\n",
    "plt.xlabel(\"$x_1$\", fontsize=16)\n",
    "\n",
    "plt.subplot(326)\n",
    "plot_predictions([tree_reg1, tree_reg2, tree_reg3], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"$h(x_1) = h_1(x_1) + h_2(x_1) + h_3(x_1)$\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=16)\n",
    "plt.ylabel(\"$y$\", fontsize=16, rotation=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "becoming-breach",
   "metadata": {},
   "source": [
    "Es más fácil usar `GradientBoostingRegressor` del Scikit-Learn para implementar este tipo de *boosting*. Funciona con árboles de decisión, así tiene hiperparámetros relevantes para los árboles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "contrary-police",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GradientBoostingRegressor(learning_rate=1.0, max_depth=2, n_estimators=3)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.ensemble import GradientBoostingRegressor\n",
    "\n",
    "gbrt = GradientBoostingRegressor(max_depth=2, n_estimators=3, learning_rate=1.0)\n",
    "gbrt.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "brutal-ordering",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GradientBoostingRegressor(max_depth=2, n_estimators=200, random_state=42)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gbrt_slow = GradientBoostingRegressor(max_depth=2, n_estimators=200, learning_rate=0.1, random_state=42)\n",
    "gbrt_slow.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "personalized-clear",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_23407/3820871828.py:3: DeprecationWarning: Calling np.sum(generator) is deprecated, and in the future will give a different result. Use np.sum(np.fromiter(generator)) or the python sum builtin instead.\n",
      "  y_pred = sum(regressor.predict(x1.reshape(-1, 1)) for regressor in regressors)\n",
      "/tmp/ipykernel_23407/3820871828.py:3: DeprecationWarning: Calling np.sum(generator) is deprecated, and in the future will give a different result. Use np.sum(np.fromiter(generator)) or the python sum builtin instead.\n",
      "  y_pred = sum(regressor.predict(x1.reshape(-1, 1)) for regressor in regressors)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, '$x_1$')"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fix, axes = plt.subplots(ncols=2, figsize=(10,4), sharey=True)\n",
    "\n",
    "plt.sca(axes[0])\n",
    "plot_predictions([gbrt], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"Ensemble predictions\")\n",
    "plt.title(\"learning_rate={}, n_estimators={}\".format(gbrt.learning_rate, gbrt.n_estimators), fontsize=14)\n",
    "plt.xlabel(\"$x_1$\", fontsize=16)\n",
    "plt.ylabel(\"$y$\", fontsize=16, rotation=0)\n",
    "\n",
    "plt.sca(axes[1])\n",
    "plot_predictions([gbrt_slow], X, y, axes=[-0.5, 0.5, -0.1, 0.8])\n",
    "plt.title(\"learning_rate={}, n_estimators={}\".format(gbrt_slow.learning_rate, gbrt_slow.n_estimators), fontsize=14)\n",
    "plt.xlabel(\"$x_1$\", fontsize=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "useful-astronomy",
   "metadata": {},
   "source": [
    "La taza de aprendizaje (*learning rate*) aplica un factor a la contribución de cada árbol.\n",
    "\n",
    "Si toma un valor pequeño, necesitamos más árboles para ajustar bien a los datos, pero las predicciones suelen generalizar mejor (esta es una técnica de regularización que se llama *shrinkage*).\n",
    "\n",
    "En la figura arriba, el modelo a la izquierda no tiene suficientes árboles (*underfitting*), mientras el modelo a la derecha tiene demasiados (*overfitting*).\n",
    "\n",
    "Una forma de encontrar el número óptimo de árboles es con *early stopping*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "defined-satellite",
   "metadata": {},
   "source": [
    "El método `staged_predict()` ejecuta una iteración sobre las predicciones del ensamble en cada etapa de entrenamiento (con $1$ árbol, $2$ árboles, etc.)\n",
    "\n",
    "El código abajo entrena un ensamble de *Gradient Boosted Regression Trees* con $120$ árboles, mide el error de validación en cada etapa de entrenamiento para encontrar el número óptimo de árboles, y después entrena otro ensamble GBRT con este número de árboles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "greenhouse-colon",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GradientBoostingRegressor(max_depth=2, n_estimators=33)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "X_train, X_val, y_train, y_val = train_test_split(X, y)\n",
    "\n",
    "gbrt = GradientBoostingRegressor(max_depth=2, n_estimators=120)\n",
    "gbrt.fit(X_train, y_train)\n",
    "\n",
    "errors = [mean_squared_error(y_val, y_pred)\n",
    "          for y_pred in gbrt.staged_predict(X_val)]\n",
    "\n",
    "bst_n_estimators = np.argmin(errors)\n",
    "\n",
    "gbrt_best = GradientBoostingRegressor(max_depth=2, n_estimators=bst_n_estimators)\n",
    "gbrt_best.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "visible-malta",
   "metadata": {},
   "outputs": [],
   "source": [
    "min_error = np.min(errors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "direct-tolerance",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_23407/3820871828.py:3: DeprecationWarning: Calling np.sum(generator) is deprecated, and in the future will give a different result. Use np.sum(np.fromiter(generator)) or the python sum builtin instead.\n",
      "  y_pred = sum(regressor.predict(x1.reshape(-1, 1)) for regressor in regressors)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, '$x_1$')"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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BDQEws78SRsLf0czmRyNYA1wDHGFhiqYjotd5o2RORJJJ85p3JbC/mU0nzH95sbsvKUzEIlKK8j43q7tPICRs8etuj3vuwHkpjj0lxfqlRHe2hdCzp5I5EUkujWveAuDr+Y5LRMqH5mbNgi22gM8+A02mISIiIvmmZC4LttgC1q+HlSsLHYmIiIhUGiVzWbDFFmGpqlYRyZe6Orj66rAUkcqW9zZz5Sg+mRswoLCxiEj5W7kSDjsM1q2DDh3g2WehpqbQUYlIoahkLgt69gxLlcyJSD6sWBESuY0bw3LSpEJHJCKFpGQuC2Ilc599Vtg4RKQydOsWSuSqq8OytrbQEYlItmXSlELVrFmgNnMikk9duoSq1UmTQiKnKlaR8lJX17QpRXOUzGWBkjkRybeaGiVxIuVq0qTMmlKomjULOnUKmbOSOREpFPVuFSkftbWZNaVQyVwWmDUOHCwikm/JqmRUaidSumpqMmtKoWQuSzQ/q4gUSrIqGSVzIqUtk6YUqmbNknbt4M03VcUhIvmXaZWMiJQXlcxlQV0dzJgB9fWhqkNVHCKST5lWyYhIeVEylwWTJoF7eK4qDhEpBPVuFalcqmbNgtraUL0BquIQERGR/FIylwU1NTBqVHj+2GO6OxaRRmZ2pJnNMrM5ZnZJku3/z8ymRo8ZZrbRzLZoy3tqmBKRyqJq1izZZ5+wHDSooGGISBExs2rgFuAIYD4wxczGu/s7sX3c/Xrg+mj/Y4Gfunur+8ZrmBKRyqOSuSzp0ycsFy8ubBwiUlT2Aea4+wfuvg64Hziumf1PAf7aljfMdOR4ESl9SuaypHfvsFy0qLBxiEhR6QvMi3s9P1rXhJl1Bo4EHmnLG2qYEpHKo2rWLImVzCmZE5E4lmSdp9j3WOCVVFWsZjYSGAkwYMCApCeoqwslcWPGwNKlGqZEpFIomcuSWMmcqllFJM58oH/c637AghT7nkwzVazuPhYYCzBs2LAmCaHayolULlWzZknHjtC9u0rmRGQTU4AhZjbYzDoQErbxiTuZ2ebAwcBjaZ31zTehW7fGx4UXqq2cSAVTMpdFvXurZE5EGrn7BmA08BQwE3jQ3d82s1FmNipu1+OBp919ZVonrq+HL79sfNx3n9rKiZSwtg4npGrWLOrTRyVzIrIpd58ATEhYd3vC67uAu9I+6Z57wgsvhCK4Xr1g6VJq9nOefdY0pZdIiUlsIlF3+1t8dbNZGZ1DyVwW9ekDc+cWOgoRKXtVVaF6FcJyxQr44gtqajZXEidSYuKbSHRbu4Rdz9obNq7P6BxK5rKod2947bVCRyEiFaVXr5DMLVkCm29e6GhEJEOxJhLr1sF27eZRvXY99OgBRxyx6Y4PPZTyHErmsqhPn3A9ra8PN84iIjm35ZahSmDJEth++0JHIyIZqqkJvc8nTYJvdvsczgd23x0efHDTHS3ZSEeBkrks6t0bNmyAzz+HLdo0s6KISJp69QrLRx9t2s5j7703SfBi49CpTZ1Icampib6Tjy4PK3r0yOh4JXNZFD9wsJI5EcmLrbYKy2uuabqtXz+YFyag0Dh0IiXg88/DMsMmE0rmsih+4OChQwsbi4hUiAsvBHdYu3bT9Q88APPnN7T7SDYOnZI5kSITS+ZUMlc4mtJLRPJut93g7rubrh8/HlavhjVroHPnTRpZaxw6kSK1XNWsBRdL5jRwsIgUXKdOIZlbtQo6d96kkbXazIkUmTVrQqncgmi2PyVzhRNrh6ySOREpuM6dYdky/v3yap6e2ZjAKYkTKTKffw5DhoQe6TFqM1c47dtDz54qmRORItC5MwBnnbyKtzeo04NI0ZozJyRy7dqFoYZ69Qq9lTKg0dCyrHdvlcyJSBHo1AmA9utXbdLpQUSKzLp1YTlsGCxcCDNmwKBBGZ0i78mcmR1pZrPMbI6ZXZJku5nZTdH2aWa2V0vHmtkeZjbZzKaa2etmtk++Pk8izc8qIkUhKpnr1m411dXq9CBStGLJXIcOrT5FXpM5M6sGbgGOAnYGTjGznRN2OwoYEj1GArelcex1wG/cfQ/g8uh1QVRVwTvvhDGdREQKJkrmbrl+FVdeqSpWkaIVG1aoY8dWnyLfbeb2Aea4+wcAZnY/cBzwTtw+xwH3uLsDk82sh5ltAwxq5lgHukfHbw4syMNnaaKuDl55JYzjdNhhuniKSAFFydzOg1ax8zcLHIuIpFZqJXNAX2Be3Ov50bp09mnu2AuA681sHvB74NJkb25mI6Nq2NcX56CXwqRJYXxOUPsUESmwqM0cq1YVNg4RaV5UMvfuhx1bXauX72Qu2SyxnuY+zR17DvBTd+8P/BT4U7I3d/ex7j7M3Yf1jk3XkEW1taFHK4Sl2qeISMFEJXOsXp3xoXV1cPXVai4ikg+z3w4lc1Pf6cBhh7Xue5fvZG4+0D/udT+aVomm2qe5Y88A/hY9f4hQnZt3NTVwww3h+XXXqYpVRFru9BXtUxt14HrbzF7IyhvHkrmEkrmWErXYHK6XXUar/7GISPpmTQ/J3Frv0OpavXwnc1OAIWY22Mw6ACcD4xP2GQ+cHvVq3Q9Y7u6ftnDsAuDg6PmhwOxcf5BUhg8Py65dCxWBiBSLdDp9mVkP4Fbgm+6+C3BSVt48Vs36//5fGLtqyy1Zv/mWDNi/Hy/96qmUiVqyOVxFJHsSb6h22j5Us66zjq3udZ7XDhDuvsHMRgNPAdXAOHd/28xGRdtvByYAw4E5wCrgzOaOjU79Q+BGM2sHrCH0gi2Ifv3ADD76qFARiEgRSafT16nA39z9YwB3z87gRvvvD2PGhGrWqKq1PaGh8bH1j/L0um8waVLTGgTN4SqSO3V1cMghjd+v55+Hmn6hZG6vfTvw7P+0rlYv7zNAuPsEQsIWv+72uOcOnJfusdH6l4GvZTfS1unQAbbdVsmciADJO27tm7DPV4D2ZjYJ6Abc6O73JJ7IzEYS3agOGDCg5Xf+9rfDNEGxYQ+AD659iO2uP4fN7YuUiZrmcBXJnXvuafxKrl0bXtdEJXNf278jtPL7pum8cmDAACVzIgKk1+mrHeFm9DCgE1BnZpPd/b1NDnIfC4wFGDZsWOI5kuvadZM2H9sdsC1cD3vv+AXPjkudqGkOV5E8KsGhSSrCwIHw8ceFjkJEikC6nb7+6e4r3X0J8CLw1ZxE0z0MxzmkzxdK1kTyLNZGrl270ByrQwc4/XSUzBWrgQNh3rzGMedEpGKl0+nrMeBAM2tnZp0J1bAzcxJNlMyt/HS5hh4RyaNYL/E774TqavjRj2hss1qCM0BUhIEDQ6K9cGFoPycilSmdTl/uPtPM/glMA+qBP7r7jGzFUFcX1/6tz+YALJrzBZddFgoCNFONSO7F9xKH0Byr4XuXhZI5JXM5EGub/NFHSuZEKl1Lnb6i19cD12f7vWOlAbGecy883J29gW7+xSZDjyiZE8mtZnuJZ6FkTtWsOTBwYFiq3ZyIFFLimHHP/ztUs3bnC6qrXEOPiORJrJf4lVcmKQ1XyVxxiiVz6tEqIoWUWBpw4OEd4bcd6LBuHYt7DGGzzkan01s4Sf/+MH68RkIXaaOUvcSVzBWnbt2gZ08lcyJSWEnHjNt7b3jlFXouex+WpXGSOXPgX/+CQw/NbbAilUodIIqXxpoTkWLQpDTg+efhww8BuP9+eOop+MY34OSTkxx85pnwyiuwYUM+QhUpP8uXw7nnwqLUE7us+/c0OgCz5nZgx1a+jZK5HBk4EObOLXQUIiIJ2reHIUMYOxZ+dHlYddcr8MVWMDJxIsRoKBMlcyKt9OST8H//1+wuscrVs68cxPWHlsh0XpWiQwd4773Qm0w9xUSk2DzySNPXTZK5dtG/CCVzIq2zZElYfvObMHp0k81//SvcfTd8Ur81Mzfs1ure5UrmcqCuDh57DNavD8MCaBwnESk2J5wATz+96esmlMyJpG2TMR1j//OXRQ1Td98djjiiyTGDusKL96cYsiQDSuZyYNKkxoEBNY6TiBSjWCncI4+ERK5JqRwomRNJU+KYjmPGwNKlMOLtZWwDsMUWSY9L2kmpFZTM5UBtbWiWsnZtuBZqHCcRKUYjR6ZI4mKUzImkJX5Mx7VrQ41qfT0MYBmnQcpkDpoZsiQDGjQ4B2pqQj04wE9/qlI5ESlR1dVhqWROpFmxMR2rq6GqKiR1GzdCz41Lww7NJHPZoJK5HDnmGDBr07AxIiKFFSuZi7UbEZGmVqygpu5OZp2ynI8+hE6dwpA/Gx12Yzo4SuZKVfv2sPXWMH9+oSMREWklVbOKtOy+++DCC+kP9I9WfS1xn759cxqCkrkc6tdPyZyIlDAlcyIt++yzsDzgADj88Kbbhw6FQYNyGoKSuRzq1y+MNSciUpKUzIm0LDa36iGHwK9/XZAQ1AEih1QyJyIlTcmcSMtiyVyHDs3vl0NK5nKof/8wLduKFYWOREQKxcyONLNZZjbHzC5Jsr3WzJab2dTocXkh4kxKyZxIy9avD8v27QsWgpK5HOrXLyxVOidSmcysGrgFOArYGTjFzHZOsutL7r5H9PjvvAbZnCiZmzRxA3V1BY5FpFipZK68KZkTqXj7AHPc/QN3XwfcDxxX4JjSNn9hSOaef2YDhx2GEjoRwvfg6qvjvg9FUDKnDhA5pGROpOL1BebFvZ4P7JtkvxozewtYAFzk7m8n7mBmI4GRAAMGDMhBqE3NndeOfkCVb9DUhCI0nbbr2WehRiVz5W3bbcNSyZxIxbIk6zzh9RvAQHf/KvC/wKPJTuTuY919mLsP6927d3ajTGHg9uF+v4NtaNMk4CKlqEkJHJtO2xW7wWkomStgMqeSuRzq2BH69FEyJ1LB5tM4jihAP0LpWwN3/yLu+QQzu9XMern7kjzFmNKA7cK/iNoDN1B7jUrlpHIkLYGraZy2K7a+thaYHpXMqQNE+dLwJCIVbQowxMwGm1kH4GRgfPwOZra1mVn0fB/CdXlp3iNNJuoAUTNsgxI5qShJS+AICd2zz8KVVzYmeMXQAUIlcznWrx98+GGhoxCRQnD3DWY2GngKqAbGufvbZjYq2n47cCJwjpltAFYDJ7t7YlVsYSQMTVJXF/6p1daqlE7KW9ISuEhNTcLfv6pZy1+/fvDyy4WOQkQKxd0nABMS1t0e9/xm4OZ8x5WW6uqw3LAhZbWTSDmKlcCldfOyTtWsZa++HpYtg+efL3QkIiIZipXMbdyYstpJpFzV1MCll6Zx01IEJXNK5nKorg7GjQvPhw/XGE0iUmLiqllj1U7V1U2rnUQqWhGUzKmaNYcmTWqcBUdjNIlIyYlL5jKqdhKpJEVQMqdkLodid7Jr1oS7Wd3Jikgxa9LBIaEDRJOG3yKi3qzlrqYGnn4aDj4YTj1VF0ERKV5JOzgkJHMikkQRVLPmvc2cmR1pZrPMbI6ZXZJku5nZTdH2aWa2VzrHmtn50ba3zey6fHyWdBx4IAwYEBoNi4gUq6QdHJTMibSs0qpZzawauAU4gjAy+hQzG+/u78TtdhQwJHrsC9wG7NvcsWZ2CGHy6t3dfa2Z9cnfp2rZwIEaa05EilvScbX+o2ROJJVYs4SfrljHZlA5yRywDzDH3T8AMLP7CUlYfDJ3HHBPNGjmZDPrYWbbAIOaOfYc4Bp3Xwvg7ovy9HnSMmiQhiYRkeKWtIPDE0rmRJKJb5bw/fr19IOK6s3aF5gX93o+ofStpX36tnDsV4ADzewqYA1wkbtPyWLcbTJwIHzySSiJLeDvWkSkWU06OKiaVSSp+GYJ7am8DhCWZF3itDWp9mnu2HZAT2A/YG/gQTPbLnFKHDMbCYwEGDBgQAZht82gQWHw4PnzYfDgvL2tiEjbKJkT2dRHH8E77/CtjvBaNWxw6Fy/KmyroJK5+UD/uNf9gAVp7tOhmWPnA3+Lkrd/mVk90AtYHH9idx8LjAUYNmxY3uY+HDgwLD/6SMmciJSQWDJXVwe77cbK1cZLu57L5hePUu98qTxr1sCee8Jnn7ET8Gji9o4d8x9TJN/J3BRgiJkNBj4BTgZOTdhnPDA6ahO3L7Dc3T81s8XNHPsocCgwycy+Qkj8luT6w6Rr0KCwVCcIESkp228fShtWrYIZM+gCDH3/GnZ+epTmZpXKM3MmfPYZbL550z/+gw6CLl0KExd5TubcfYOZjQaeAqqBce7+tpmNirbfTpiQejgwB1gFnNncsdGpxwHjzGwGsA44I7GKtZD69wezUDInIlIy+vcPDX4XLuRPd9Zz+v8OYwAfU712FZMmdVYyJ+XnzTdhzpzk2159NSyPOAIeeih/MaUh74MGu/sEQsIWv+72uOcOnJfusdH6dcD3shtp9nToANtso5I5ESlBvXtD797sfAq8f/MODPV3udXO5eC5O8Cai2CzzQodoUh2LFgAw4aFRu7N2W23/MSTgbSTOTPrQBgC5Fl3n5G7kMrToEEqmROR0lVTA0sO2wMmvsv3N94NdwKH7gAnn5z2OZpMFyZSTBYuDInc5puH0rdkunWDH/4wv3GlIe1kzt3Xmdk1wDdyGE/ZGjgQJk8udBQikm9mdiRwI6F5yB/d/ZoU++0NTAa+6+4P5zHEtNTVwZRh/8Oxu/8Xg996NAxKl8EdatLpwpTQSTGJzeSw445FV43akkyn85oJbJeLQMrdoEEwb56m9RKpJHEz1xwF7AycYmY7p9jvWkKb4KITS8R+dv027HLbaD7ceXjYsGABdXVw9dVhn+YknS5MpJisK/x4ca2VaTJ3OXCZmRVfhXGRGzgwDNX0i1+0fNETkcIzs2fMrMm31cx2M7P1ZpbYEz+Zhllvora9sZlrEp0PPAIU1ew1MYmJ2NRF2wKwdPoCDjsMLrssJHvNXdti04VVV8dNFyZSTCoombsY6Aq8GU12/5KZvRj3eCEHMZaFVdGYgr//fcsXPREpCi8De5lZw+BRZmbArcCr7v5/aZwj1Yw2DcysL3A8cDvNMLORZva6mb2+ePHi5nbNusREbIeDQjLX/o3J/HTN1XTYuKrF0rbYdGFXXqkqVilSJZzMZdqbdSObzqMqaVq4MCzr6xurGHQxEylqrxDGrNyT0JYN4HTCTDN7pXmOdGa9GQNc7O4bQ66YXKEGPYem87bu2n87GG10Xz6fq/gFH9sAHulwWoulbU2mCxMpJpWSzLl7bY7iKHvf+hZcf314rioGkZIwmXADux8w2cx6ANcBN7v79DTPkc6sN8OA+6NErhcw3Mw2uPujrQ89+zZNxPrB44+HxnKvvML3j17Gub9QoiYlroSTuUyrWaWVamrg8MOha1eYOFEXPZFi5+5fAm8RkjmAq4B64NcZnKZh1ptoeKeTCbPcxL/PYHcf5O6DgIeBc4stkUvq6KMbLmRfP3C1rmlS+iopmTOzbczs92Y2xczeN7N/mdl1ZrZ1LgIsJ9/6FqxYEQYQFpGS8Aqwn5ntBYwC/p+7f5Huwe6+AYjNXDMTeDA2601s5puS1qlTWMYaBYuUslgy1759w6p0e2sXWkbVrNG8py8BPQkXuTnA1sBPgNPN7EB3n531KMvEf/1XWL7yCgweXNhYRCQtLxN6mt4DvOLuf8n0BC3NepOwfkQrYiyczp3DcvXqhlUaGFhKVmycuahkrpTGRsy0A8S1wBfAvu7+YWylmQ0Eno62fztr0ZWZXXeF7t3h5Zfhe0U7+ZiIxHklWg4l/U4PlSOhZK6U/vmJNJFQzZpsbMRi/XvOtJr1EOCy+EQOwN0/Aq6ItksK1dWw//4hmRORkvAlsI7Q6WFaoYMpOgklcxoYWEpJkyrUhGSulMZGzLRkrgOwIsW2FdF2acYBB8CvfhUG2Rw+vHizfBEBwkDpy8is00PliJXMRclc7J9frGSumP/5SWVLWoqckMwlDslTzP+vM03mpgLnm9mT7l4fWxkNpHlutF2a0aNHWP7ud3DDDaqGECk2ZtYZ+CpwIKE98EnuvrywURWphGrWUvrnJ5UtaRXq+qa9WUtlbMRMk7n/Bp4AZprZA8CnhA4QJwFDgKOzG175WbIkLDV4sEjROhx4DPgE+Im7/73A8RSvJB0gSuWfn1S2pKXI/yjdoUkyHTT4n2Z2DPBb4JeE0c0d+DdwjLs/nf0Qy8vXvw6/+U14rmoIkeLj7uNJPnODJMpwaBL1dJVikbQU+e8VkMyZWXtgODDN3YdFVRE9gc/cXYMMpammJnSCmD0bHn1UFzQRKWEZDE2inq5SbJqUIicZZ65UpN2b1d3XAw8Cg6LXq9z9EyVymTvgAPjsMxg2rNCRiIi0QUIHiFjCdtllYRk/0Kp6ukrRSxhnrpRk2mbuA6BPLgKpJLvsEv5mZs+GnXcudDQiIq0US+bmzoVjjqH3HHhodWh7Y6uh95nw2ZawdCmc2gH28DAf2nrvyOBtLwP2KFzsIolKeDqvTJO564Bfmtlz7r44FwFVgl12Ccu331YyJyIlbKutQkK3ahX84x/sAOwQv31WWPSMXg6Mra8HXtkSzhibp0BF0lBBydyhwBbAXDObTOjN6nHb3d3PyFZw5WroUDALydxJJxU6GhGRVurWDaZNg3ffbVg1812YMR123S0s//IX2FgP1VVh5puTtn4JrrsOlmu0FymA1avhjTfCkBKJPvkkLCsgmTsQWA8sBraPHvG8yRHSROfOsN12IZkTESlpO+wQHpGdjoGdouef18EzDzV2erhkFLCUkMx9+WUhopVKd+qpofdhczbbLC+hZFOmQ5MMylEcFWfXXZXMiUh5Szr8w6SuYaOSOSmE994Ly732auyNHW/rreGQ0puZNJOhSToAk4FLNJ5c2+2yC/zjH413rCIi5ajJ8A9do2RuRaqZIUVyo64Odlqwkh4ADz0UqsjKRCZDk6wDBgMbchdO5dhlF9iwofEmQUSknMUmNX9zTrewQiVzkkexYXPWf74SgNdndilwRNmVdjIXeQb4ei4CqTSxHq1XXbXpWEwiUl7M7Egzm2Vmc8zskiTbjzOzaWY21cxeN7MDChFna8WStOauY/Hjz510pqpZJf9i4xx2ISRzk6Z0Setvt1Rk2gHif4G/mFk74FGa9mbF3T/ITmjl7bPPwvKBB+CxxzQaukg5MrNq4BbgCGA+MMXMxrv7O3G7PQuMd3c3s90Jg7MPzX+0mUt3Vof4AYOXeUjmNiz/kuuv1tRekh+1tdCxfT2dN4YBrrtv3bmsZiTJtGTuBaA/8LPo+XvA7ISHpCF2J+Cu0dBFytg+wBx3/yBqqnI/cFz8Du7+pbvHboq7UEKjAqQ7q0NsUvPqaljfIVRvVa36kst+5U1mihDJhZoaeO4fIZGr77AZSz+rKqsZSTItmTszJ1FUoNpa6NgR1q6FqqrwWkTKTl9gXtzr+cC+iTuZ2fHA1YQZdo5OdiIzGwmMBBgwYEDWA22NWJIWK91IdR3btFdrO9YftBntN6yhc/0KVq3rzqRJpV0qIqVh311DFWtVty5p/+2WikyHJrk71baoOmHzNkdUIWpq4Lnn4Nvfhu7dYb/9Ch2RiOSAJVnXpOTN3f8O/N3MDgKuBA5Pss9YYCzAsGHDiqL0LunQI83sG9u+vmtX+HwNHzOAwe0XUltbeuN6SQlaGZI5unTJ6G+3FLRYzWpmy8xsr7jXZmbjzSyxT+8wwmDCkqb994ff/CbM0XrOOapqEClD8wlNU2L6AQtS7ezuLwLbm1mvXAeWLTU1cOmlmf0zbH/GaQD0YDnP3T2v5P+RSnGLdXSY+uqqsKJLqOpvzd9usUqnzVwPNi3BqwKOidZLGw0ZEpZ33IHajoiUnynAEDMbHI3VeTIwPn4HM9vBzCx6vhfQgTBPQvkaMwZ22w2APXdcVdhYpKyNHQsHHQS/+hX8+OzGkrlyk2mbOcmy114L87TGd4Qoh7sEEQF332Bmo4GngGpgnLu/bWajou23AycAp5vZemA18N24DhHlq1OnsFy9urBxSHlauZLp/zede86Fr20Mq3Zb90Z4omROsi3WCHPt2tDTq9QbYYrIptx9AjAhYd3tcc+vBa7Nd1wFF5tKaVUomaurK5/2S1IEjjiC3erqeDl+XewWKTYLSRlRMldgNTXwzDPw9a/rIiYiFSSWzK1enfZ4dSJpmzULgDfsa6zzdpjBoEGw1bbtYPTowsaWA+mOM9fXzLaLOj1sl7guWt8vnROlMRq6mdlN0fZpCZ0vWjr2IjPzUmo8DHDggXDKKfDqq6GETkSk7MWqWVetSnu8OpG0RdX36ye+wPO/m0z9K5PZ6oPJ8PLLcOSRBQ4u+9ItmXs4ybpHE14bLQx2meZo6EcBQ6LHvsBtwL4tHWtm/aNtH6f5mYrKSSfBn/8MI0fCqFG6KxWRMhdXMlduY35Jgbk3JHP71nZi30MLHE8epJPMZXOg4IbR0AHMLDYaenwydxxwT9QAeLKZ9TCzbYBBLRz7B+DnwGNZjDdvYu0x77kHHnpI1QwiUubiSubKbcwvKbA1a8KyQ4cwKn8FaDGZa26g4FZIZzT0ZPv0be5YM/sm8Im7vxX18E+qGEdQj3nllcbn6tUqImUvKpmb+Phqunx100GFRdok1kM6VvpbAfKdsqYzGnqqfZKuN7POwC+By1t6c3cf6+7D3H1Y7969Www2n2LVDADt2qmaQUTK2/xloWTuhSdXaYxNya5YMhcr/a0A+U7m0hkNPdU+qdZvDwwG3jKzD6P1b5jZ1lmNPMdqauAf/wglwiecoDtUESlv7y8IpSYdfbU6PUh2KZnLuRZHQ49enx71at0PWO7un6Y61t2nu3sfdx/k7oMISd9e7r4wb58qSw4/PHTP//e/Cx2JiEhuDdwpJHNdbZU6PUh2VWA1a17HmUtzNPQJwHBgDrCKqANGqmPzGX8+fPObcP758N578JWvFDoaEZHcGLRTKDX51uC3OPq0exkyh3DVT1RVFe5yty6pyhYppGgg6koqmcv7oMFpjIbuwHnpHptkn0Ftj7Jwjj02JHMXXACXXabqVhEpU5tvDsCgD56DK59rft+jjoIJzV76pYRlffaPCqxm1QwQRWbBgjBX65NPhj9uDVEiImXp2GPDXeuSJan3+eILGD8ePvwwX1FJnuVk9g9Vs0qhxTcC1hAlIlK2unWDP/yh+X0++SQkc59/npeQJP+Szf7R2v95sRK+b7OaHUElc1I4tbXQsWMY87CqSo2CRaSC9egRlkrmyla2Zv+Y/OI6Rn79I9avh+VVc7kGlMxJ4cRGQj/uOBgwQKVyIlLBOncOA2+uXh0mru7YsWFT1ttZSUEkm/2jNb/bgafUMH3tG+FFfbRS1axSSPvvD+ecA1ddBYsWQZ8+hY5IRKQAzELp3JIloXRuq62AHLWzkoKJn/2jVb/b9evZZkFI5GazA2aw7eDN6HzKKbkNvIhUxqRlJeikk6C+HkaO1MjoIqXMzI40s1lmNsfMLkmy/TQzmxY9XjWzrxYizkKoq4Orr27hGtezZ1jGVbUma2cl5aFVv9tlywBYv/mWPPy72Sx+ZTad358Ohx6ay1CLikrmitSKFeGm9LHH4Omnk9+dXHHFFTz88MPMmDEj7fOOGDGCJUuW8MQTT2Q5YhFJZGbVwC3AEYQBzaeY2Xh3fydut7nAwe7+mZkdBYyl6ZzVZSftEphYu7lnnw0dIoBvdoUXq2GDQ7vq8JrngD32gC22yM8HkJxoVRu6KJlrv9WWXHppLqMrXkrmisyIESO4++67GTbsbOCPQGgqMmkS/P3vP+f666/n6KOP5oknnuCiiy7i/PPPz+j8N954I2EoPxHJg32AOe7+AYCZ3Q8cBzQkc+7+atz+kwlTEpa9tHsxxpKz8xqHH90FeDL2Yh3w4+j50KEwc2aOIpZ8SNaGriUzXljKrsCKDlvSLcfxFSslc0Wof//+vPPOA3TseCNr1nShvh6ef34Db7xxLwMGDGjYr2vXrnTt2jWjc28eDdQpInnRF5gX93o+zZe6nU1cnlLO0i6BufDC0OZkw4bUJ6uvhxde0Hh0ZSK+DV1L6urgf36yjIeAl9/Zgh51ldl+Um3mitDuu+/OjjsO4Wc/e5Czzw7Vrc888w+WLduMXXapbdjviiuuYNddd214PWLECI455hhuvPFG+vbtS8+ePTnzzDNZFZvaJG6fmNraWs455xwuvPBCtthiC3r37s2NN97I2rVrOe+88+jRowcDBgzg3nvvbTjmww8/xMx4/fXXN4nbzHj44Yc32ef+++/n4IMPplOnTuy5555MmzaNGTNmsP/++9OlSxcOOOAA5s6dm+0foUixsCTrkhaNm9khhGTu4hTbR5rZ62b2+uLFi7MYYmHESmCuvLKFRu5HHBHamjz3XOrHs8+Gfdety1v8kgNLlsD06S0+3vrLdP74k7B8+/7pDF0/HYDFvmXFtp9UyVyROvvss7n//nEMH34mVVWwceM43M9k4cIP2Hbb1Me99NJLbLPNNkycOJF58+bxne98h6985Stc2kxDgvvuu4+f/exnvPbaa4wfP54LLriAf/7znxx55JG8/vrr3H333fzgBz/gsMMOY9vm3jyJX//61/zhD39gu+2245xzzuHUU0+ld+/eXHXVVfTp04czzjiDH//4xzz++OMZnVekRMwH+se97gcsSNzJzHYntKs4yt2XJjuRu48ltKdj2LBhZdFWIpMSmGZVV4e73vr6UG9bXZ2Fk0peffopDB4c2hW14KvRg7glwOdVW1bs2KxK5orUqaeeGrWJm0379t3YuPGfwP8yf/7lzY6D2L17d2677TbatWvHTjvtxEknncSzzz7bbDK3yy67cMUVVwDws5/9jGuuuYb27dvzk5/8BIDLL7+ca6+9lldffZUTTzwxo8/xs5/9jOHDhwNw4YUXcuyxx/LII49wyCGHADB69GhGjx6d0TlFYmLjUW25JSxdmnpZWwuhqWjffM/WPgUYYmaDgU+Ak4FT43cwswHA34Dvu/t7eY6vfHToEBKB9euVzJWi2bPD769zZ9huu5S7LVoM//lP42sjFHWvsi70+/mpFVnFCkrmilbPnj05/vjjefPNcZx5Zg8ef7yWBQsGsHhx+OeUqiv/zjvvTLt2jb/Wbbfdltdee63Z99p9990bnpsZffr0YbfddmtY1759e3r27MmiRYsy/hzx594qGiMq/txbbbUVK1euZNWqVXSuoAEeK0lLCVfXrvDuu2He9S++CJ0Xly+HYcNCYcuUKWHb559D9+7w2WfhmJdfhtdeiyVp6dq6b04+ZAruvsHMRgNPAdXAOHd/28xGRdtvBy4HtgRuNTOADe4+LJ9xloVYMrduHWy2WdJdNNBwEVu5MiwPOACeeirlbu/H9YKuqgpNKd2hyuC3ldr7ASVzRe2ss87ijDPOoGvXrhxwwH/z0ENhfegQkfyY9u3bb/LazKivr0++czPHNHeeqqrQ1DK+V+z69etbPHf0jyrpupZilOKUmKjFqjgmTQoJ2DPPwBNPNN92vdy5+wRgQsK62+Oe/wD4Qb7jKjux60qKdnMaaLjIxdp2d+nSbNId39v188/huuvC+vr6cB2qVErmithhhx1Ghw4dWLJkCaNGfYvHHguz2kBoB7poUePffz717t0bgE8//bRh3dSpU/MfiLRKcwlYstKzJUvCne/HH4cEbfnyMEf6rFnhBjp2Z2zWWLuVjeTNLLNSt9j+icuqqjAjlBmsXatxecpWhw5hmeLGMtVgtCqpKxJRydzilZ1bTLpjbS2vvjp8v+vrw3Jp0tamlUHJXBEzM6ZNm4a70717R559Ngy1NHs23H9/bJ/wzzmfF6JOnTqx3377ce2117L99tuzfPnyZtvkSXGoq4N77oFx48L/u8QEbOPGTKssN+XechKXKuFqLgFbvz5crFPtc9ZZsOeeLbeZA9h///806XwgZSKWzKUomUscCmXLLVVSV1Sikon5n3VpSLrXrAnXrFS/l9raMF1vRgMMlyklc0WuW7fGRgA1NbD77qFk5Msvwzr3ZgbbzKFx48bxgx/8gL333pvtt9+eW2+9lYMOOii/QVSQVO3OWipViy3feKMxiYuXTgKWrqqqxk6FGzY03i2nm3C15rNlXqLyycLsfFopOi1UsyYORpv2oMWSH1HJ3FbbdabdtMaby3Hj4PTTk/9uampgzBh45BE44YTK/v1Zpc4GMGzYME8cJ61U1NXBwQeHf8zt2sEPfpD6j11KUyx569QptI988snG6syYWKlaLHlqzVc5lmxBYwKWaelZfKKWLAErpiosM/t3OXQuKOXrV87svDPMnMnU+97myY92bvHvTm3oisyVV8Lll8Mvf8k5S3/LHXeE60x1ddiUrPKn0n6HzV2/VDJXgmpqwjiZxx8f2jPdeSfcfXf5/yGXipZ6b7ZU4vTaa3DvvSmb/jRoTamaWSjAaCkBy6T0LNUds0heRdWso85ax+sbWv7n3pppoySHYr1Zu3Th9KPD/7SWqk9VutpIyVyJOuAAOPlkuPlm/SEXi2Rt0hKZNY5t2lrxJWOJ1ZrplKI1V2UhUrKialZbv46N9eldE7M2aLG0XSyZ69w57UQ77SnhKoCSuRJ26qkwdmz4Q3YP0xKOHVt8VVulpLVt01K1SUvknnl1aHPtzjIpVdPfhJS1qGSuU7v1VG/UP/eSEzc0CaSXaKt0tZGSuRJWUxP+iC+8MCQhY8eG9WZhzMxyrXbNZNR/SG/f7t3DILSPPNI0ITMLCVWsBCwT2eql2dKFqhx/zyLpqquDbT/twEDgf29Yx/gV+udeKmLX8x9+tJJeEGaAyIBKVwMlcyWupgaOPTa0s4pV3bmH8eiuuCI8amqKb+TzTEvAliwJyc/kyTBxYnpDYLQ2AUvkHqqy05GsTVp+emmKVKZYI/hHV4dkztavS9pYXorIuHFw002sXOl0eR+GO7Tnw7AtKpmTzCiZKwOxsXbWrt20LdbTT4fSuf32g3/9KyQkHTu2vcSuLcNkdO8Or74KDz2UvHdmIRKwVBJLyiB127R02qQlUrIm0naxRvDrCG3m3p66np3TPLbYbnIrxk03wVtv0QXYPW51vVVRNXRooaIqaUrmykB8u4EttwxVhc8805jQvPJK476rV8Nll8F3vrNpAvaHP9zHiy/+kkWLPmbAgAFcddVVbLfdaU0SsxdeCAMWp2rAn+mo/fFak4C11OAf0h9yo61t0/QPQST/Yo3g168ObeZ2HxrGmWspUau0YS0yldNEN+rs8O514znjsgGsXx9qNG55eCuG7bh1lt+sMiiZKxPx7QZ22w1eeimMnp0ssXr22fCIjVNWX38f9fUjgdAA9aOPPmLEiJHRoI2nZRRHaxK51paApTvqfyZDbqhtmkhpid3Mbv6jDjAddhy8Lq1ETcNapJbzRDdK5oaeuhdjDujbkDQO08+/1So2mZs1axa1CV2dvvOd73DuueeyatUqhg8f3uSYESNGMGLECJYsWcKJJ57YZPs555zDd7/7XebNm8f3v//9JtsvvPBCjj32WGbNmsWPfvSjJtt/9atfcfjhhzN16lQuuOCCJtt/97vfsf/++/Pqq6/yi1/8osn2MWPGsMcee7By5USGDv0tCxfCwoWNydCuu97BjBk74v44cEPcOGWTgbWbnGvDhlXA2cCdcWsfBnoBd0WPTbVvP4Gqqs6sW3cr7g822W42KYrl98ATbL11mONz/Xro3LkTp532JLW18Oc/X8nEic/Svj0Nd2zt22/Jj3/8CEuXwsyZlzJzZh0zZzaeu1+/fvzlL38B4IILLmDq1Kk89VTj9q985SuMjXqIjBw5kqeeem+T2PbYYw/GjBkDwPe+9z3mz5+/yfaamhquvvpqAE444QSWJkwCeNhhh3HZZZcBcNRRR7E6Nolu5JhjjuGiiy4CaPJ3B+Xztzdx4kR++9vfNtl+xx13sOOOO/L4449zww03NNl+77330r9/fx544AFuu+22JtsffvhhevXqxV133cVdd93VZPuECRPo3Lkzt956Kw8+2PRvb9KkSU3WSfmoqQG+2h6mA+vXp5WoaViL1HKe6MZ6rkbDkCiJbruKTebKXffu4bH11vD559CjB/z856FEK77ELpR4rU1xlqbrY23a+vRpTMRiSdef/hR60V5zDbz77qbb2reHESNCCdijj4Yks3v3xvN26tQ4wvfEiTBgwKbvu+WWMHJkeH7ppWHSdxGRBnFzsyZL1BKrDTWsRWo5T3QThiGRttN0XhUmsfNCbS0cf/wg/vOfj5LsPZBRoz5M2n5MFz4pRZrOq4ydcw7cfjvceiucc84myRuofVymctZmbv368Euorg7PzbJ48vKm6bykQbIi7RtuuIqRI0eyKna3BLRv35lf/OIqrrgiv/GJlBszOxK4EagG/uju1yRsHwr8GdgL+KW7/z7/UZaBaAYI/vlPWLGCGqCmGngJnnsefrwG6h2q1sDq/wYOSXKO6mo48UQYODB/cRepnFV/xlWxKpHLHiVzwmmnhU4OZ599NmvXrmXgwIFcddVVDetFpHXMrBq4BTgCmA9MMbPx7v5O3G7LgB8D38p/hGWkR4+wHD8+POIcGj0AcOCf0SOZujp4+OFcRCjQpIpVw8Nkh5I5AUJCd+edobODGouLZM0+wBx3/wDAzO4HjgMakjl3XwQsMrOjCxNimTjvvNCoN66GId4nC2Dex9B/APTdNskO8+aFcZeWLMltnJUurmROw8Nkj5I5EZHc6QvMi3s9H9i3QLGUt622orl2IX2jR0qTJ4dkbs2aLAcmm4hL5jQ8TPYomZMGv/vd7wodgki5SdYoqFW9zsxsJDASYEBid29pu802C0slczkRq049ptdKdgPo0kXDw2RR3pO5NBoDW7R9OGEU2xHu/kZzx5rZ9cCxwDrgfeBMd/88Lx+ojOy///6FDkGk3MwH+se97gcsaM2J3H0sMBZCb9a2hyabUDKXG0uW8MakLzj7e6Hz6nvV7/NnaBhjTsPDZEdek7k0GwMfBQyJHvsCtwH7tnDsM8Cl7r7BzK4FLgUuztfnKhevvvoqoKROJIumAEPMbDDwCXAycGphQ5KklMxl36RJcOih7OXe2Eg0NhVk585ADnvNVph8l8y12Bg4en2PhwHwJptZDzPbBhiU6lh3fzru+MlA0yHypUWxkf3VAUIkO6IbzNHAU4QahXHu/raZjYq2325mWwOvA92BejO7ANjZ3b8oVNzlJq0ek0rmsu+558CdDd16Mu/LHg2zEW3drx2dTj+90NGVlXwnc+k0Bk62T98U65M1JD4LeKDNkYqIZIG7TwAmJKy7Pe75QkL1q+RA2j0mO3YMy7hkTsNmtNG77wLQ7pYbWbjD9xt+loP1s8y6fCdz6TQGTrVPi8ea2S+BDcB9Sd9cDYhFRCpK2j0mE0rmSn3YjDYlomvXwtFHw+zZm6xasxY269iY97Zo4cKwHDqUmr1L6+dXavKdzKXTGDjVPh2aO9bMzgCOAQ7zFHOUqQGxiEhlSbvHZCxDWbsW3Jk0yUp22Iw2J6LTp4eD4nSMHhnbZhvYZZfWHCkZyHcyl05j4PHA6KhN3L7Acnf/1MwWpzo26uV6MXCwuycfMVJERCpO2j0mq6oas75166it7Viyw2a0efy2L78My332gQcf5JZb4IYbYGM9VFfBhReGMZrT0qcPdOqU2QeQjOU1mUunMTChbclwYA5haJIzmzs2OvXNhJuGZ8LIJkx291H5+2TlYcyYMYUOQUQkKxKrGWtqwrqrr24mqdtss5D9rFlDTU3Hkh02o83jt8WSuV69YOBA9joeFt7ceL69jgc0fW1Ryfs4c2k0BnYgac6f7Nho/Q5ZDrMi7bHHHoUOQUSkzZJVM0IaVY+bbQZffBHazW2+eZNhM0qlQ0Sbx2+LJXNdujR85jFjYOnS4v/slUozQEiDiRMnAnD44YcXOBIRkdZLVs0IaVQ9NjM8Sal1iGjT+G0rVwKwaFXXkvrMlUzJnDT47W9/CyiZE5HSlqqascWqx2aSuYqaRzQqmft4WdfK+cwlTsmciIiUlVTVjC1WPcaSuc8/h9WrG1a/9hp8+gF0qYKNDh3aQ21tGTfqj5K5rYd0pcPU0uwEUmmUzImISNlJVs3YYtVjLJnbb79NVu8bPW6KrVgD3HQy1Pw1K7HmSqvb+EXVrP127FqynUAqjZI5ERERgOOPhxkzoL6+YdX6DbBhQ+Mu7dpB+w1r4G9/CxvatfxvtBAdJ9rUxi+uA0Smbe9KpZNIuakqdAAiIiJF4ZJLQqnU6tUNj9dfXM2WnVbTrTosX39xNfTvH7KkuXNbPGUsqbrssrCsq8vD5yB1J5C0xJK5rl0zes9CfVZRyZzEueOOOwodgohIXrVUkpS0/d1OO8G8efD1r0OXLs2ef4fF8K9Y87vVsMXRsLh9OKxz56b7r1oV8slU29P1k1XwzfpoLsx6GHwnKSa6TGJeNA16hslcRXUSKTJK5qTBjjvuWOgQRETyJt2qyCZVjbW18PTT8OGHLb5H7+jR4LPm9+8cPdqqM9AwiZYDLRcibqqqCnbeOaND2jxYsbSakjlp8PjjjwNw7LHHFjgSEZHca3VJ0iWXwIknhnlc0zB1KkyZEuadf/jhxmmxRo+GH/6wcb8774Sbb069Pddice69N+xxRG/YaquU+yYr0WzzYMXSakrmpMENN9wAKJkTkcrQ6pIkMxgyJO332WNX2ON70XRijze+364nA7s27rfryTD7ztTbc6muDg4bmVBKmSKXa65Es02DFUurqQOEiEgOmdmRZjbLzOaY2SVJtpuZ3RRtn2ZmexUizkoUK0m68sr8zG7Q0vvlO554mXSYaFPnCskJlcyJiOSImVUDtwBHAPOBKWY23t3fidvtKGBI9NgXuC1aSh7kuySppfcrVMlWJqWUahtXfJTMiYjkzj7AHHf/AMDM7geOA+KTueOAe9zdgclm1sPMtnH3T/MfrsRrqadrsYyplo04MmnvprZxxUfJnIhI7vQF5sW9nk/TUrdk+/QFlMwVUEs9XTMdlDdXiV+bBgdOkEmpoNrGFRclc9Lg3nvvLXQIIuXGkqzzVuyDmY0ERgIMGDCg7ZFJs1rq6ZpJT9hsJlyZxtkaxVLiKOlTMicN+vfvX+gQRMrNfCD+i9UPWNCKfXD3scBYgGHDhjVJ9iS7WmoXlkm7sVwOpltbG2YUq68Py7a2X8tl4im5o2ROGjzwwAMAfPe73y1wJCJlYwowxMwGA58AJwOnJuwzHhgdtafbF1iu9nKF11K7sEzajeW6w4D7psu20CwOpUnJnDS47bbbACVzItni7hvMbDTwFFANjHP3t81sVLT9dmACMByYA6wCzixUvLKpbPU8zWWHgUmTQuLlHpZtTb7UU7U0KZkTEckhd59ASNji190e99yB8/Idl+RXrjoMZJJ8pdMWTj1VS5OSORERkRKVbvKVSVs49VQtPUrmRERESlg6yZfawpU3TeclIiJSgurq4Oqrw7IlserY6mq1hStHKpmTBg8//HChQxARkSQS27tlOoSI2sKVNyVz0qBXr16FDkFERBIkS9xaU22qtnDlS9Ws0uCuu+7irrvuKnQYIiISJ1nilqtq00yqbqV4qGROGsQSuREjRhQ0DhERaZRs+JFcVJtq9ofSpWRORESkiNXUwJgx8MgjcMIJjQlWtqtN1eO1dCmZExERKWJ1dXDBBSHBeukl2G23wg9ALMVFbeZEREQKJJ02aslKzHIhVnV75ZWqYi01KpkTEREpgHTbqDVXYpbOFF1S/pTMSYMJEya0vJOIiGRFum3UUnV2yHaHBXWAKF1K5qRB586dCx2CiEjFyKSNWrLODtnusKAOEKVLyZw0uPXWWwE499xzCxyJiEj5a+vwItnusKAOEKVLyZw0ePDBBwElcyIi+dKW4UWyPdacpvwqXUrmRERESlS2x5rTlF+lKe9Dk5jZkWY2y8zmmNklSbabmd0UbZ9mZnu1dKyZbWFmz5jZ7GjZM1+fR0QkmXSvS2Y2zswWmdmMfMcoIuUhr8mcmVUDtwBHATsDp5jZzgm7HQUMiR4jgdvSOPYS4Fl3HwI8G70WESmkdK9LdwFH5isoESk/+S6Z2weY4+4fuPs64H7guIR9jgPu8WAy0MPMtmnh2OOAu6PndwPfyvHnEBFpSVrXJXd/EViWp5hEpAzlu81cX2Be3Ov5wL5p7NO3hWO3cvdPAdz9UzPrk+zNzWwkobQPYG2JVGv0Apbk8w3NrDWH5T3ONiiVWBVn9u2Yx/dK67qUroTr15dmNqutAaahlH63zSmXzwH6LMUqH59lYKoN+U7mkmUJnuY+6RzbLHcfC4wFMLPX3X1YJscXguLMvlKJVXFmn5m9nuXzTQS2TrLpl9l8H9j0+pUvpfS7bU65fA7QZylWhf4s+U7m5gP94173AxakuU+HZo79j5ltE939bgMsymrUIiJJuPvhqbaZma5LIpIX+W4zNwUYYmaDzawDcDIwPmGf8cDpUa/W/YDlUVVFc8eOB86Inp8BPJbrDyIi0gJdl0QkL/KazLn7BmA08BQwE3jQ3d82s1FmNirabQLwATAHuBM4t7ljo2OuAY4ws9nAEdHrluS1uqINFGf2lUqsijP78hlr0uuSmW1rZg0TIZvZX4E6YEczm29mZ+cxxpaU0u+2OeXyOUCfpVgV9LOYe0bNzkRERESkiOR90GARERERyR4lcyIiIiIlrOKSuZamEyskM+tvZs+b2Uwze9vMfhKtL8rpysys2szeNLMnotdFF6eZ9TCzh83s3ejnWlOkcf40+p3PMLO/mtlmxRJnsummmovNzC6Nvl+zzOwbBY7z+uh3P83M/m5mPQodZzHL5G8u8ftfTNL5HKmut8Wipf9VUSfBpFNfFpM0PsdpUfzTzOxVM/tqIeJMR7r5g5ntbWYbzezEfMVWUcmcpTedWCFtAC50952A/YDzoviKdbqynxA6o8QUY5w3Av9096HAVwnxFlWcZtYX+DEwzN13BaoJvbWLJc67aDrdVNLYor/Xk4FdomNujb53hYrzGWBXd98deA+4tAjiLGaZ/M0lfv+LSTqfI9X1tuDS/F+VdOrLYpLm55gLHBx9R6+kSDtFpJs/RPtdS+ismTcVlcyR3nRiBePun7r7G9HzFYQLZV+KcLoyM+sHHA38MW51UcVpZt2Bg4A/Abj7Onf/nCKLM9IO6GRm7YDOhDEUiyLOFNNNpYrtOOB+d1/r7nMJvdL3KVSc7v501BMeYDJhfMqCxlnk0vqbS/H9LyYtfo5mrrfFoC1TXxaTFj+Hu7/q7p9FL+O/o8Um3fzhfOAR8jyuZKUlc6mmCis6ZjYI2BN4jYRpgYA2TQuUJWOAnwP1ceuKLc7tgMXAn6PqoD+aWReKLE53/wT4PfAx8ClhbMWnKbI4E6SKrZi/Y2cBT0bPiznOQkr3b24MTb//xSSj707C9bYYpPP3WQp/w5nGeDaN39Fi0+JniWpZjgduz2NcQP5ngCi0Nk8Jlg9m1pWQ2V/g7l9Y6+ZKzRkzOwZY5O7/NrPaAofTnHbAXsD57v6amd1IcVT9biJqz3McMBj4HHjIzL5X0KBaryi/Y2b2S0K12n2xVUl2K3ic+WBtnIKsWL7/bf0ccefZ5HqbjdiyoC1TXxaTtGM0s0MIydwBOY2o9dL5LGOAi919Y77/b1daMpfOdGIFZWbtCReW+9z9b9HqYpsW6L+Ab5rZcGAzoLuZ/YXii3M+MN/dY3fbDxOSuWKL83BgrrsvBjCzvwH7U3xxxksVW9F9x8zsDOAY4DBvHFiz6OLMlyxMQZb0++/ueb0BycZUaimut8WgLVNfFpO0YjSz3QlV9ke5+9I8xZapdD7LMOD+KJHrBQw3sw3u/miug6u0atZ0phMrGAt/AX8CZrr7/8RtKqppgdz9Unfv5+6DCD/D56ILebHFuRCYZ2Y7RqsOA96hyOIkVK/uZ2ado7+Bwwjtd4otznipYhsPnGxmHc1sMKFx9r8KEB8Qep8BFwPfdPdVcZuKKs4i0uLfXDPf/2LS4udo5npbDNoy9WUxafFzmNkA4G/A9939vQLEmK4WP4u7D3b3QdF342Hg3HwkcrE3r6gHMJzQq+194JeFjichtgMIxbbTgKnRYziwJaFH1uxouUWhY42LuRZ4InpedHECewCvRz/TR4GeRRrnb4B3gRnAvUDHYokT+CuhLd96wt3p2c3FRqjmeh+YRbjTLmSccwjtXGLfp9sLHWcxP1L9XoFtgQlJ9m/4/hfTI53Pkep6W+jY4z5Dk/9VwChgVPTcCL0r3wemE3rDFzzuVnyOPwKfxf0OXi90zK39LAn73gWcmK/YNJ2XiIiISAmrtGpWERERkbKiZE5ERESkhCmZExERESlhSuZERERESpiSOREREZESpmROss7M3MxuiHt9kZldkaVz32VmJ2bjXC28z0lmNtPMnk9YP8jMTs31+4uIiKRLyZzkwlrg22bWq9CBxDOz6gx2P5sw4OMhCesHAUmTOTOrtBlVRCQHzGwHM1tvZr9JWH+bma0ws2GFik2Kk5I5yYUNwFjgp4kbEkvWzOzLaFlrZi+Y2YNm9p6ZXWNmp5nZv8xsupltH3eaw83spWi/Y6Ljq83sejObYmbTzOxHced93sz+jzCwZmI8p0Tnn2Fm10brLicMKHq7mV2fcMg1wIFmNtXMfmpmI8zsITN7HHjazLqY2bgojjfN7LgW4tvGzF6MzjfDzA5s5c9cRMqEu88hDKb709hNcXRdOgs43t1fL2R8UnxUkiC5cgswzcyuy+CYrwI7AcuAD4A/uvs+ZvYT4Hzggmi/QcDBwPbA82a2A3A6YTqbvc2sI/CKmT0d7b8PsKu7z41/MzPbFrgW+BphBPKnzexb7v7fZnYocFGSi+Yl0fpYEjkCqAF2d/dlZvY7wvRGZ5lZD+BfFiYEPy1FfN8GnnL3q6KSw84Z/LxEpHz9hnBdu9jM3gV+DZzi7hMLG5YUIyVzkhPu/oWZ3QP8GFid5mFTPJpb0MzeB2LJ2HQgvrrzQXevB2ab2QfAUODrwO5xpX6bE+bbXAf8KzGRi+wNTPLGCe7vAw4iTPuViWfcfVn0/OuEScgvil5vBgxoJr4pwDgLE34/6u5TM3xvESlD7r7QzMYAFxL+V//Y3R+MbTezXxDmnR0CfNvzNQeoFCUlc5JLY4A3gD/HrdtAVL0fTXTdIW7b2rjn9XGv69n0bzVxDjonzFN4vrs/Fb/BzGqBlSnisxbiT1f8+Q04wd1nJcSRNL5o20HA0cC9Zna9u9+TpbhEpLTNJszT/LK735Kw7VngAeBPeY9Kio7azEnORKVVDxI6E8R8SKjWBDgOaN+KU59kZlVRO7rtCBOlPwWcE5VwYWZfMbMuLZznNeBgM+sVVXGeArzQwjErgG7NbH8KOD9K3jCzPePWN4nPzAYCi9z9TsJFea8W3l9EKkDU1OMOoA74LzP7avx2d3/N3d8vSHBSdJTMSa7dAMT3ar2TkED9C9iX1KVmzZlFSLqeBEa5+xpCY+F3gDfMbAbhIthsyXNUpXsp8DzwFvCGuz/WwntPAzaY2Vtm1qSDB3AlIUGdFsVxZbQ+VXy1wFQzexM4AbixhfcXkTJnZnsRmnv8kXCN+Bj4XQFDkiJn7ok1ViIiIlIIUYeuV4CXgO+4e72ZnQmMAw529xcT9p8EjFGbucqmkjkREZEiYGZbEzp+zQROizp6AdwDvEsYGkmkCXWAEBERKQLuvpDQDjhx/UbCsE0iSamaVUREpMSY2a+AUUBvQsesNcCwKCGUCqNkTkRERKSEqc2ciIiISAlTMiciIiJSwpTMiYiIiJQwJXMiIiIiJUzJnIiIiEgJUzInIiIiUsKUzImIiIiUMCVzIiIiIiVMyZyIiIhICfv/nrL8cvxgroIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 4))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.plot(np.arange(1, len(errors) + 1), errors, \"b.-\")\n",
    "plt.plot([bst_n_estimators, bst_n_estimators], [0, min_error], \"k--\")\n",
    "plt.plot([0, 120], [min_error, min_error], \"k--\")\n",
    "plt.plot(bst_n_estimators, min_error, \"ko\")\n",
    "plt.text(bst_n_estimators, min_error*1.2, \"Minimum\", ha=\"center\", fontsize=14)\n",
    "plt.axis([0, 120, 0, 0.01])\n",
    "plt.xlabel(\"Number of trees\")\n",
    "plt.ylabel(\"Error\", fontsize=16)\n",
    "plt.title(\"Validation error\", fontsize=14)\n",
    "\n",
    "plt.subplot(122)\n",
    "plot_predictions([gbrt_best], X, y, axes=[-0.5, 0.5, -0.1, 0.8])\n",
    "plt.title(\"Best model (%d trees)\" % bst_n_estimators, fontsize=14)\n",
    "plt.ylabel(\"$y$\", fontsize=16, rotation=0)\n",
    "plt.xlabel(\"$x_1$\", fontsize=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "enhanced-conditions",
   "metadata": {},
   "source": [
    "### Stacking\n",
    "\n",
    "El último método de ensamble que veremos se llama *stacking* (*stacked generalisation*).\n",
    "\n",
    "La idea es usar un modelo para agregar las predicciones de los predictores en el ensamble (en vez de elegir algo *a priori*).\n",
    "\n",
    "![](figures_ensamble/fig7-12.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "athletic-scientist",
   "metadata": {},
   "source": [
    "Para entrenar la \"licuadora\" (*blender*) se puede usar un conjunto de *hold-out*.\n",
    "\n",
    "Primero, el conjunto de entrenamiento está dividido en dos subconjuntos. El primero está usado para entrenar los predictors en la primera capa.\n",
    "\n",
    "![](figures_ensamble/fig7-13.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "protecting-bottom",
   "metadata": {},
   "source": [
    "Después, los predictores de la primera capa realizan predicciones en el conjunto $2$ (el de *hold-out*).\n",
    "\n",
    "Así aseguramos que las predicciones son \"limpias\" ya que los predictores no vieron estos datos en su entrenamiento.\n",
    "\n",
    "Ahora, para cada instancia en el conjunto de *hold-out* hay $3$ valores predichos. Creamos un nuevo conjunto de entrenamiento con estas predicciones como *features* de entrada (por lo tanto, es un conjunto tridimensional), y manteniendo los valores de *target*.\n",
    "\n",
    "La \"licuadora\" está entrenada en este nuevo conjunto para que aprenda predecir los valores de *target* usando las predicciones de la primera capa.\n",
    "\n",
    "![](figures_ensamble/fig7-14.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "considered-stuff",
   "metadata": {},
   "source": [
    "Es posible entrenar varias \"licuadoras\", y así tener una capa de \"licuadoras\".\n",
    "\n",
    "Para hacer eso, hay que dividir el conjunto de entrenamiento en $3$ subconjuntos:\n",
    "\n",
    "* El primero es para entrenar la primera capa.\n",
    "* El segundo es para crear el conjunto usado para entrenar la segunda capa (con las predicciones de la primera capa).\n",
    "* El tercero es para crear el conjunto usado para entrenar la tercera capa (con las predicciones de la segunda capa).\n",
    "\n",
    "Una vez completado el entrenamiento, una predicción para una nueva instancia se puede obtener pasando a través de cada capa secuencialmente.\n",
    "\n",
    "![](figures_ensamble/fig7-15.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "individual-permission",
   "metadata": {},
   "source": [
    "Scikit-Learn no tiene una implementación de *stacking*, pero no es muy difícil implementar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "emerging-answer",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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