11_CART.ipynb

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    "# Analítica y Ciencia de Datos\n",
    "\n",
    "## CIDE - Otoño 2015\n",
    "\n",
    "### Árboles de Clasificación y Regresión"
   ]
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    "# Referencias\n",
    "\n",
    "Capítulo 9 de [ESL](http://statweb.stanford.edu/~tibs/ElemStatLearn.1stEd/).\n",
    "\n",
    "Capítulo 8 de [ISL](http://www-bcf.usc.edu/~gareth/ISL/)\n",
    "\n",
    "[Capítulo 11 del Handbook of Statistics, Vol 23](http://mason.gmu.edu/~csutton/vt6.pdf)\n",
    "\n",
    "[Capítulo 9 de *The Data Mining and Knowledge Discovery Handbook*](http://www.ise.bgu.ac.il/faculty/liorr/hbchap9.pdf)\n",
    "\n",
    "Un descripción a profundidad del algoritmo de *Cost-Complexity Pruning* se puede ver [acá](http://www.cs.uu.nl/docs/vakken/mdm/trees.pdf%60)"
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    "# Árboles de Decisión\n",
    "\n",
    "\n",
    "* En las notas anteriores vimos dos formas de estimar modelos no lineales: \n",
    "\n",
    "    * **Modelos no lineales de regresión**: hacer una aproximación de primer orden un modelo no lineal (en parámetros), y obtuvimos un método simple de actualización por medio de OLS iterativo.\n",
    "    * **Modelos Aditivos Generalizados**\n",
    "    \n",
    "\n",
    "* Ahora vamos a ver una clase de modelos muy simples y poderosos: *árboles de decisión*.\n",
    "\n",
    "\n",
    "* La idea es simple: los regresores $X_1, X_2, \\cdots, X_p$ generan el espacio $X_1 \\times X_2 \\times \\cdots \\times X_p$\n",
    "\n",
    "\n",
    "* Vamos a dividir este espacio en rectángulos: $R_m$\n",
    "\n",
    "\n",
    "* La estimación de $y$ en $R_m$ es la media restringida a ese rectángulo."
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    "# Ejemplo: dos regresores contínuos $X_1$, $X_2$\n",
    "\n",
    " ![caption](figures/cart_libro.png)\n",
    " \n",
    " [Figura 9.2 de ESL](http://statweb.stanford.edu/~tibs/ElemStatLearn.1stEd/)"
   ]
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    "# Aproximación de la función\n",
    "\n",
    "* En el ejemplo anterior aproximamos la función que queremos aprender como \n",
    "\n",
    "$$\n",
    "f(x) = \\sum_{m=1}^5 c_m I\\{(X_1, X_2) \\in R_m\\}\n",
    "$$\n",
    "\n",
    "\n",
    "* Podemos capturar no linealidades de los regresores que en pueden ser difíciles de capturar con otros modelos.\n",
    "\n",
    "\n",
    "* La figura muestra que el *primer corte* se hace con el primer regresor $X_1$ utilizando el punto de corte o *threshold* $t_1$.\n",
    "\n",
    "> Este corte hace una primera partición del espacio de regresores.\n",
    "\n",
    "\n",
    "* El algoritmo se llama **CART (Classification and Regression Trees)** y sólo hace cortes binarios\n",
    "\n",
    "    * En cada iteración busca simultáneamente el regresor que tiene un mayor poder predictivo y el punto de corte correspondiente.\n",
    "    \n",
    "    * En este caso la interpretación es simple: el regresor con mayor poder predictivo es $X_1$.\n",
    "    \n",
    "\n",
    "* Después explora cada lado del árbol:\n",
    "\n",
    "* **A la izquierda**: condicionamos a $X_1 \\leq t_1$ y buscamos nuevamente el regresor con mayor poder predictivo y el punto de corte correspondiente $(X_2, t_2)$.\n",
    "\n",
    "* **A la derecha**: condicionamos a $X_1 > t_1$ y buscamos nuevamente el regresor con mayor poder predictivo y el punto de corte correspondiente $(X_1, t_3)$.\n",
    "\n",
    "\n",
    "* Principal ventaja de los CART: son fáciles de explicar y de interpretar.\n"
   ]
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    "# Definiendo un árbol de decisión\n",
    "\n",
    "\n",
    "* La figura muestra.\n",
    "\n",
    " ![caption](figures/binary_tree.png)\n",
    " \n",
    "(Tomado de [acá](http://algs4.cs.princeton.edu/32bst/images/binary-tree-anatomy.png)) \n",
    "\n",
    "* Los árboles de decisión se leen de arriba hacia abajo.\n",
    "\n",
    "\n",
    "* El primer nodo es el *nodo inicial*, *base* o *raíz*.\n",
    "\n",
    "* Los **nodos finales** indican que no se hacen más cortes.\n",
    "\n",
    "* Cada nodo genera un subárbol o *subtree* del árbol inicial.\n",
    "\n"
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    "# Árboles de regresión:\n",
    "\n",
    "\n",
    "* Queremos modelar la función $f(x)$ como \n",
    "\n",
    "$$\n",
    "f(x)  = \\sum_{m=1}^M c_m I(x \\in R_m)\n",
    "$$\n",
    "\n",
    "\n",
    "* Vamos a utilizar como criterio para comparar modelos la suma de residuos al cuadrado, así que vamos a buscar minimizarla.\n",
    "\n",
    "\n",
    "* Si conociéramos las regiones, sabemos que el estimador de OLS es:\n",
    "\n",
    "$$\n",
    "c_m = \\overline{y}_{x \\in R_m}\n",
    "$$\n",
    "\n",
    "\n",
    "*  Cómo funciona el algoritmo:\n",
    "\n",
    "* En cada iteración vamos a buscar simultáneamente el regresor y punto de corte correspondiente que minimizan el SSR, condicionando en la región en la que estamos buscando.\n",
    "\n",
    "* **Primera iteración**:\n",
    "\n",
    "    1. Loop sobre cada regresor $k$:\n",
    "\n",
    "        * Loop sobre un grid de valores que puede tomar el regresor correspondiente: $t_k \\in [\\min X_k, \\max X_k]$\n",
    "        \n",
    "        * Cada $t_k$ genera dos regiones y obtenemos la media de $y$ en esa región:  \n",
    "$$\n",
    "X_k \\leq t_k \\implies c_l\\\\\n",
    "X_k > t_k \\implies c_r\n",
    "$$\n",
    "        * Obtenemos el SSR correspondiente $\\sum_i (y_i - c_l)^2 + (y_i - c_r)^2$ y lo guardamos.\n",
    "        * Buscamos la combinación $(X_k, t_k)$ que minimiza el SSR\n",
    "        \n",
    "\n",
    "* Las demás iteraciones hacen lo mismo: pero tenemos que condicionar por la región en la que estamos buscando."
   ]
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    "# Veamos un ejemplo\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import sys\n",
    "#sys.path.append('//Users//danielvaughan//Documents//Python Scripts//')\n",
    "sys.path.append('C:\\\\Users\\\\a3940004.EDIFICIOS\\\\Documents\\\\Python Scripts\\\\')\n",
    "import olsdan as ols\n",
    "\n",
    "# importemos los datos\n",
    "#data = pd.read_csv('//Users//danielvaughan//Documents//Clase CIDE//Slides//Analitica//datasets//Credit.csv')\n",
    "data = pd.read_csv(u'D:\\\\Míos\\\\Clase CIDE\\\\Slides\\\\Analitica\\\\New_CIDE_Analytics\\\\data\\\\Credit.csv')\n",
    "N = data.shape[0]\n",
    "dum_hombre     = np.asarray(data.Gender == ' Male').reshape((N,1))\n",
    "dum_estudiante = np.asarray(data.Student == 'Yes').reshape((N,1))\n",
    "dum_casado     = np.asarray(data.Married == 'Yes').reshape((N,1))\n",
    "# Para etnicidad debemos excluir una variable que sirva como referencia:\n",
    "dum_ethnic = np.asarray(pd.get_dummies(data.Ethnicity).iloc[:,:-1])\n",
    "# etiquetas de X\n",
    "labs_x = np.array(['Score','Ingreso',u'Límite de Crédito',u'Número Tarjetas','Edad',u'Educación'])\n",
    "#,'Hombre','Estudiante','Casado','Caucasian','Asian'])\n",
    "# incluyamos todas las variables:\n",
    "prexmat = np.concatenate((\n",
    "                        np.asarray(data.Rating).reshape((N,1)),\n",
    "                        np.asarray(data.Income).reshape((N,1)),\n",
    "                         np.asarray(data.Limit).reshape((N,1)),\n",
    "                         np.asarray(data.Cards).reshape((N,1)),\n",
    "                         np.asarray(data.Age).reshape((N,1)),\n",
    "                         np.asarray(data.Education).reshape((N,1)),\n",
    "                         ),axis=1)\n",
    "saldo = np.asarray(data.Balance).reshape((N,1))\n",
    "# transformemos el saldo: es positivo siempre, así que una log() nos da algo más parecido a una normal\n",
    "yy    = np.log(saldo + 0.000001)\n",
    "\n",
    "nvar = prexmat.shape[1]"
   ]
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sVrY80yl5W44FZragXOcOAgBJZ8GQPeF7uGdAISvw235EkW0NqytauSAoAUnj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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x17d000f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Por qué están tan parecidas score y límite?  Correlación altísima: casi 1-1!\n",
    "# así que eliminemos una.  \n",
    "plt.scatter(data.Rating, data.Limit)\n",
    "plt.title(u'Relación entre Límite de Crédito y Score Crediticio')\n",
    "plt.ylabel(u'Límite (dólares)')\n",
    "plt.xlabel('Score')\n",
    "\n",
    "\n",
    "prexmat = np.concatenate((\n",
    "                        np.asarray(data.Income).reshape((N,1)),\n",
    "                         np.asarray(data.Limit).reshape((N,1)),\n",
    "                         np.asarray(data.Cards).reshape((N,1)),\n",
    "                         np.asarray(data.Age).reshape((N,1)),\n",
    "                         np.asarray(data.Education).reshape((N,1)),\n",
    "                         ),axis=1)\n",
    "labs_x = np.array(['Ingreso',u'Límite de Crédito',u'Número Tarjetas','Edad',u'Educación'])\n",
    "nvar = prexmat.shape[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 368,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "la primera variable es:  Límite de Crédito\n",
      "el punto de corte es:  3189.51666667\n"
     ]
    },
    {
     "data": {
      "image/png": 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2T+FMXDURH3cfXuzxotmhCGGK6yZ/rfVprfUO+/MrwD6gITAYyCpxOAsYYn9+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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ed85910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# primera iteracion\n",
    "# Tamaño del grid\n",
    "G = 100\n",
    "# Queremos guardar los resultados acá\n",
    "SSRMat = np.zeros((G,nvar))\n",
    "for k in range(nvar):\n",
    "    # seleccionemos la variable\n",
    "    xk    = prexmat[:,k].copy()\n",
    "    # el grid va a ser sobre los percentiles 5% y 95%\n",
    "    q05   = np.percentile(xk,5)\n",
    "    q95   = np.percentile(xk,95)\n",
    "    gridk = np.linspace(q05,q95,G)\n",
    "    # empezamos el loop sobre el grid\n",
    "    for t in range(G):\n",
    "        dum_kt = np.asarray(xk>gridk[t]).reshape((N,1))\n",
    "        xmat   = np.concatenate((np.ones((N,1)), dum_kt),axis=1)\n",
    "        olstk  = ols.ols_dan(yy, xmat)\n",
    "        # guardemos el ssr\n",
    "        SSRMat[t,k] = olstk.ssr()\n",
    "\n",
    "# guardemos el menor, y el threshold correspondiente\n",
    "ssr_min = SSRMat.min()        \n",
    "var_min = np.dot(((SSRMat==ssr_min).mean(axis=0)>0),np.arange(nvar))\n",
    "# ahora el threshold\n",
    "xk    = prexmat[:,var_min].copy()\n",
    "q05   = np.percentile(xk,5)\n",
    "q95   = np.percentile(xk,95)\n",
    "gridk = np.linspace(q05,q95,G)\n",
    "ixmin = np.argmin(SSRMat[:,var_min])\n",
    "thr_min = gridk[ixmin]\n",
    "print 'la primera variable es: ', labs_x[var_min]\n",
    "print 'el punto de corte es: ', thr_min\n",
    "\n",
    "# grafiquémoslo\n",
    "SSRMat = pd.DataFrame(SSRMat, columns = labs_x)\n",
    "SSRMat.plot()        \n",
    "plt.legend(loc='best', fontsize=10)\n",
    "ymin, ymax = plt.ylim()\n",
    "plt.plot([ixmin, ixmin],[ymin,ymax], ls='--')\n",
    "\n",
    "#guardemos el threshold, y la variable\n",
    "Nodes = list([[var_min,thr_min]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 369,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "la segunda variable es:  Límite de Crédito\n",
      "el punto de corte es:  2724.14393939\n"
     ]
    },
    {
     "data": {
      "image/png": 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3V5pFQVKBU/l4cH4kP1ZVD4pIR+A7EdkNzMeWb18uIlcAbwM1lAdzXkxMjON2\ndHQ00dHR5R4vUeWllBQ+CgvDz9OPmyNv5pV1r/D8lOcd29xwAzzySN2rQp5/vm1t1gkTKj92331w\n6aVw4oTtdl0ugjK1awzDddz83Gg7oS3HvjlG8DXBzd2dJvfTDz+xKm0V7WNqXympzqWGRWQ+kA3M\nV9VAe5sAJ1S1jYg8DKCqT9kf+xbbB0IS8JOqhtrbZwATVPX2CvuvdSHv/xw5wj+SklhrT4Ynnkhk\n+OvDSZqbhL/nydVZ3noLoqOhT586vUQyM6tfSCQhAW680XYRVHKybRaOMzl5Zxbyrk7oK6F8duVn\nhHWsvB6mYZyuUt9M5fj3xxn00aDm7goAe+bs4dDHzi+m0hDWXCt9nu9D1zm2ZIiI1L/UsIj4Am6q\nmiUifsBk4K/APhGZoKo/A2cDe+xP+RL4UERewJaO6QesU1UVkUwRGQWsA2YCi5x5QQcLCnggLo4S\ne/Bfn5XF38os6NuzbU8m9JjAB1s+4I6RdzjaZ81yZu+V1VSArlcv+OknePFFeOkl26ybxmbSNYZR\nWYcLOxA/Lx5roRWLZ/POBs9cn8mR/xxh5LaRWLyapi/u7ZxLxDizVTCw3D67xR1YYp9RcxR4RUS8\ngDzgVgBV3SkinwA7OTm1snQIOwfbFEofbFMonTrpuiYzk315edxrXwh4RnAwF1RY0PXuUXdzx9d3\ncPuI26ucieNKFostXdMYC4RUxZx4NYzKPIM98R3oy4mfT9BuUt0W83AlVSVuXhw9F/TEK6TlTems\nNciragIQUUX7BmBUNc95Eqg0e1xVNwJ1HvvG5+Uxpk0brg6uPvc2occEPN08+T7+eyb1ccmpgRah\n2FpMfnE+fh7OrRFpGKeT9he358h/jjRrkD+24hhFh4vofGMj1jZpgFPiite4/Hz6eNc8XUhEuDvq\nbl5Y+wJ1Pc/QkmUWZBLoFdjo304M41TU4aIOHP3yaLP9zVuLrcQ9GEfvp3tjcW+Z4bRl9qqCuLw8\netvXW6zJNUOu4WjuUa7/4nryi6soDt+M6lu7xuTjDaN6vqG+WLwsZG/Obpbjp7+XjkdHD9qfX/ss\nl+bSIpf/qyg+L48+TgR5Hw8fYm+M5cYvbuSc989h+VXL6eRX//UTXakh0ydNPt4wqiYidJjegZ0z\ndjZLPjx7czZDvx3aor9pt/ggX2y1cqCggJ61pGtK+Xr48tHlHxETG8OoN0cRe0MsPdrWfx3F5laa\nrjEMo2qXuQ/rAAAgAElEQVQ9/9qTdtOaJyfv0d4D/3D/2jdsRi0+yO8vKCDY0xOvOqyUbhELf534\nV7ILs1m8fjFPT3q6EXvYuEy6xjBq5ubjRtDZQc3djRarxefknU3VVGVW5Cz+ve3flFhP3dVrTLrG\nMIyGaPFB3pmZNdUZ1GkQXfy78GPCjy7uVdPJyM8g0NOkawzDqJ+WH+SdnFlTnZlDZ/LB1g9c2KP6\nSUiIqdfzMgsyzUjeMIx6a/FBviHpGoAZQ2bw5Z9fkl3YPFOsSiUlLajX88zSf4ZhNESLD/INSdcA\ndPLrxLge4/h81+cu7FXTMUv/GYbREC06yKsq8Q1M14AtZfP+lvdd1KumZcoMG4bREC06yB8tKsIi\nQjtnFmitwYX9L+SPg3+QnJlc+8YtTGZBpknXGIZRby06yMfl59O7AamaUj4ePlwedjlLti5xQa+a\nlplCaRhGQ7ToIN/Qk65lXTvkWpZuX+qSfdWHqV1jGEZzaNFBPs6FQf6sM84iLTuNfcf2uWR/dVXf\n2jWmrIFhGA3RsoO8i9I1AG4WNy4ZeAmf7fzMJftrKiZdYxhGQzgV5EUkUUS2isgmEVlXpv0uEdkl\nIttF5Oky7Y+IyF4R2S0ik8u0DxeRbfbHFtZ2XFemawAuC7uMz3adOkFeVckqyDIjecMw6s3ZAmUK\nRKvqsdIGEZkIXAQMVdUiEelobw8DrgLCsK3x+r2I9LMvAfgqMEtV14nIChGZWtMSgK5M14Bt9aj4\n4/EknUg6JSpTZhdm4+3ujbulxdeRMwyjhapLuqZiweQ7gH+oahGAqh62t18MLFXVIlVNBPYBo0Sk\nCxCgqqXfBN4Hpld3sPySEo4UFdHNy3U1oj3cPLh4wMWnzIVRJh9vGEZDORvkFduIfIOIzLa39QPG\ni8haEYkVkRH29hCg7IT0ZGwj+ortKfb2KiXk53OGtzduLi7G31wpm/rUrjH5eMMwGsrZPMBYVT1o\nT8l8JyK77c8NUtUzRWQk8AnQ2xWdiomJYU9uLtbMTGLz8oiOjnbFbgE4p9c5XPf5daRmpRISEOKy\n/dYmKWlBnWfYmOmThmFUJTY2ltjYWKe2dSrIq+pB+7+HRWQ5EIVtVP65vX29iFhFpAO2EXr3Mk/v\nZt82xX67bHtKVceLiYlhUXIyQbm5RPfv79QLcZaXuxfn9z+f5buWc2fUnS7dt6uZkbxhGFWJjo4u\nN/hdsKD6Aoi1pmtExFdEAuy3/YDJwDbgC+Bse3t/wFNVjwBfAleLiKeI9MKW1lmnqmlApoiMEtuC\niDPt+6jkmp07eS011aUnXcu6LPQyPt31aaPs25VMTt4wjIZyZiQfDCy3L1TrDixR1ZUi4gG8LSLb\ngELgegBV3SkinwA7gWJgjn1mDcAc4F3AB1hR3cyaC9q354L27ZnSrnHWbZzSZwo3/ecmkjOT6RbY\nrfYnNBOTrjEMo6HkZPxtGUREm6JP9357L+4Wd56d/GyjHwsgNlaIjq7b63pu9XMczDrI81Oeb6Re\nGYbRGogIqlrlLJUWfcVrY5p75lze2vQWGfkZTXK8+tSuMbXkDcNoqNM2yPdo24Np/abx2sbXmuR4\n9aldY3LyhmE01Gkb5AHmjZnHwt8XUlBc0NxdqZJZ+s8wjIY6rYN8ROcIBnUcxIfbPmzurlTJTKE0\nDKOhTusgD7bR/HNrnsOq1ubuSiUmXWMYRkOd9kH+3N7n4unmyTd7v2nurlRiplAahtFQp32QFxHu\nGXUP/9r4r0Y9jqldYxhGczjtgzzAFWFX8Nv+30jJrLLKgkskJVV/2XF1zEjeMIyGMkEe8PP04/Kw\ny3lvy3vN3ZVyTE7eMIyGMkHe7pZht/D2prdbzAnYguICrGrF2901yx8ahnF6MkHebmTISHw8fPgl\n6Zfm7gpwMh8vLq6nbxjG6cUEeTsRYVbkLN78483m7gpg8vGGYbiGCfJlXDf0Or7a8xUn8k+4fN91\nrV1j8vGGYbiCCfJldPDtwJS+UxrlCtg6rwplpk8ahuECJshXcHPEzXyw9YPm7oZJ1xiG4RJOBXkR\nSRSRrSKySUTWVXjsfvvSf+3KtD0iIntFZLeITC7TPlxEttkfW+i6l+E6o7qNYsehHTR3nf207DQ6\n+XVq1j4YhnHqc3Ykr0C0qkaqalRpo4h0ByYBSWXawoCrgDBgKrBYTk4ReRWYpar9gH4iMtUFr8Gl\n2nq3xd3iztG8o83aj11HdjGww8Bm7YNhGKe+uqRrqprL9wLwYIW2i4GlqlqkqonAPmCUiHQBAlS1\n9JvA+8D0Ova3SfQK6kX88fhm7cPuI7sJ7RDarH0wDOPUV5eR/PciskFEZgOIyMVAsqpurbBtCJBc\n5n4y0LWK9hR7e4vTO6i3y4N8XWvXmJG8YRiu4GyQH6uqkcA04E4RGQc8ApSdF9hqrtrp3db1Qb4u\ntWuyCrI4mnuUM9qc4dI+GIZx+nF3ZiNVPWj/97CILAcmAL2ALfZ0ezdgo4iMwjZC717m6d2wjeBT\n7LfLtldZESwmJsZxOzo6mujoaKdejKv0DurN+tT1TXrMsv48+if92/fHzeLWbH0wDKPlio2NJTY2\n1qltaw3yIuILuKlqloj4AZOBBaoaXGabBGC4qh4TkS+BD0XkBWzpmH7AOlVVEcm0fxCsA2YCi6o6\nZtkg3xx6B/Xm4x0fN9vxdx/ZbVI1hmFUq+Lgd8GC6jMFzozkg4Hl9hG7O7BEVVdW2MYx31BVd4rI\nJ8BOoBiYoyfnI84B3gV8gBWq+q0Tx29yjZGTrwtz0tUwDFepNciragIQUcs2vSvcfxJ4sortNgJD\n6tjHJndGmzM4mH2QopIiPNw8mvz4u47s4sqwK5v8uIZhtD7mitcqeLh5EBIQwv6M/S7bZ11q1+w+\nspvQjmYkbxhGw5kgXw1Xp2ycrV1TbC0m7lgc/dr1c9mxDcM4fZkgX43GmEbpjPjj8YQEhODj4dPk\nxzYMo/UxQb4azXXyddfhXSZVYxiGy5ggX43eQb2JP9H0QX73kd0MbG+mTxqG4RomyFejuUbyu4+a\nk66GYbiOCfLVcHWQd7Z2za7DpmaNYRiuY4J8Ndr5tKPEWsLxvOMu2Z8ztWtU1VwIZRiGS5kgXw0R\nafKUTVp2Gh5uHrT3bd9kxzQMo3UzQb4GTR3kzSjeMAxXM0G+Bk0d5E0NecMwXM0E+Ro0x0jeBHnD\nMFzJBPka9A7qTcKJhCofW31gNZGvRTq94LcztWv+PPonA9oPqFMfDcMwauLUoiGnq+pG8tvSt3HJ\nx5dwIv8Ex/KOOXWi1JnaNcmZyWY1KMMwXMqM5GvQo00PDmQeoNha7GiLPx7PtCXTWDh1IX3b9eVg\n9kGXHS81K5WQgBCX7c8wDMME+Rp4uXsR7BfMe5vf44vdX/DZzs+Y/MFkHhv3GFcPvpou/l1IzUp1\nybFyi3LJK8qjnU87l+zPMAwDnEzXiEgikAmUAEWqGiUizwIXAIVAHHCTqmbYt38EuNm+/d2lK0mJ\nyHBsK0N5Y1sZ6h6XvppGcPuI2/nvnv867t975r3cMfIOAEICQjiY5ZqR/MGsg4QEhGBfgcswDMMl\nnM3JKxCtqsfKtK0EHlJVq4g8BTwCPCwiYcBVQBi2NV6/F5F+9iUAXwVmqeo6EVkhIlNb6hKApR4d\n92i1j3Xx7+KydI1J1RiG0Rjqkq4pN8RU1e9U1Wq/+zvQzX77YmCpqhapaiKwDxglIl2AAFVdZ9/u\nfWB6vXveAnQJcD5dU1vtGhPkDcNoDM4GecU2It8gIrOrePxmYIX9dgiQXOaxZGwj+ortKfb2U1ZI\nQIjTI/naateYIG8YRmNwNl0zVlUPikhH4DsR2a2qqwBE5DGgUFU/bLRetlBd/Lu4LCdvgrxhGI3B\nqSCvqgft/x4WkeVAFLBKRG4EzgPOKbN5CtC9zP1u2EbwKZxM6ZS2p1R1vJiYGMft6OhooqOjnelm\nk6tLuqY2qdmphHcOd8m+DMNo3WJjY4mNjXVqW6ntik0R8QXcVDVLRPywnXBdgC3V8zwwQVWPlNk+\nDPgQ2wdBV+B7oK+qqoj8DtwNrAO+BhZVPPEqIursVaTNLacwhw7PdiD30dxaZ8XExgrR0dW/ronv\nTeSJ8U9wdq+zXd1NwzBaORFBVasMQs6M5IOB5fYg5g4sUdWVIrIX8MSWvgFYo6pzVHWniHwC7ASK\ngTllovYcbFMofbBNoWzRM2tq4+fph6ebJxkFGbT1btugfaVkpph0jWEYLldrkFfVBCCiivZ+NTzn\nSeDJKto3AkPq2McWrfSCqNqCfE21a1TV5OQNw2gU5orXBnL2gqiaatdkFWYBEOAZ4KpuGYZhACbI\nN5grTr6WjuLN1a6GYbiaCfIN5IqrXk2qxjCMxmKCfAO5on6NCfKGYTQWE+QbqIt/F1KzXZOuMQzD\ncDUT5BuoS4BzV73WVLsmNSuVrgGndIUHwzBaKBPkG8jZ+jU11a4xI3nDMBqLCfINVDpPviFX6Zog\nbxhGYzFBvoECvAIQxDHXvT5MkDcMo7GYIO8CIQEh9Z4rX3q1a5eALi7ulWEYhgnyLuHsydeqHM8/\njo+HD74evi7ulWEYhvP15I0aOHNBVHW1a0yqxnAlc9X06aEu5wBNkHcBZ9I11dWuMdUnDVc7VUp1\nG/VT1w9yk65xgYasEGVG8oZhNCYT5F2gLmu9VpSalUqIvwnyhmE0DhPkXaAhlSjNSN4wjMbkVJAX\nkUQR2Soim0Rknb2tnYh8JyJ7RGSliLQts/0jIrJXRHaLyOQy7cNFZJv9sYWufznNoyGVKFOzTZA3\nWg9/f//m7oJRgbMjeQWiVTVSVaPsbQ8D36lqf+AH+/3SNV6vAsKAqcBiOXmm4FVgln1VqX4iMtVF\nr6NZOVOJsrraNWYkb7QmrprdU1xc7JL9GHVL11T87V0EvGe//R4w3X77YmCpqhapaiKwDxglIl2A\nAFVdZ9/u/TLPOaUFegVSbC0muzC72m2qq11jgrzRGsXGxhIdHc0VV1xBaGgo1113neOxFStWEBoa\nyogRI7j77ru58MILAYiJiWHmzJmcddZZ3HDDDRw5coTLL7+cqKgooqKiWL16NQA///wzkZGRREZG\nMmzYMHJyclBV5s2bx5AhQxg6dCiffPJJs7zulsjZKZQKfC8iJcBrqvoGEKyq6fbH07Et+A0QAqwt\n89xkoCtQZL9dKsXefsoTEccFUf3aV7v0bSVWtZKenW6udjVapc2bN7Nz5066dOnC2LFjWb16NcOG\nDeP2229n1apV9OjRg2uuuabc6H/37t38+uuveHl5cc0113DvvfcyduxY9u/fz9SpU9m5cyfPP/88\nixcvZvTo0eTm5uLl5cXnn3/Oli1b2Lp1K4cPH2bkyJGMHz+ezp07N+M70DI4G+THqupBEekIfCci\nu8s+qKoqIi6bnBsTE+O4HR0dTXR0tKt23WhK58rXJcinZ6fTxrsNnm6ejdgzw7BpSCalPlPvo6Ki\nCAmxfUuNiIggISEBX19fevfuTY8ePQCYMWMGr7/+ur1/wkUXXYSXlxcA33//Pbt27XLsLysri5yc\nHMaOHcu9997Ltddey6WXXkrXrl357bffHB8YnTp1YsKECaxfv97xLaG1iY2NJTY21qltnQryqnrQ\n/u9hEVkORAHpItJZVdPsqZhD9s1TgO5lnt4N2wg+xX67bHtKVccrG+RPFfU5+bopbRNDg4c2Uo8M\no7ymvkaqNFgDuLm5UVxcXClnX/HCLV9f33KP/f7773h6lh8EPfTQQ1xwwQV8/fXXjB07lv/9739V\n7qs1X/1bcfC7YEH1pcxrzcmLiK+IBNhv+wGTgW3Al8AN9s1uAL6w3/4SuFpEPEWkF9APWKeqaUCm\niIyyn4idWeY5p7xgv2AO5RyqfcMyVh9YzehuoxupR4bRsogIAwYMID4+nqSkJAA+/vhjRzCuGKQn\nT57MokWLHPc3b94MQFxcHIMGDeLBBx9k5MiR7N69m3HjxvHxxx9jtVo5fPgwv/zyC1FRURjOjeSD\ngeX2X4Q7sERVV4rIBuATEZkFJAJXAqjqThH5BNgJFANz9ORvbw7wLuADrFDVb134WppVJ79ONQb5\nqmrXrElew/2j72/MbhlGkyo7eq5qJO3t7c3ixYuZOnUqfn5+jBw5EovF4ti+7HMWLVrEnXfeSXh4\nOMXFxUyYMIHFixezcOFCfvrpJywWC4MHD+a8887Dw8ODNWvWEB4ejojw7LPP0qlTp8Z/wacAaWl1\nLkREW1qfnPHahtfYkLqBNy56w6nti63FBD0dRNLcJNr5tGvk3hmnCxFp8bVrcnJy8PPzA+DOO++k\nf//+3HPPPc3cq1NHVb9je1uV+SlzxauLdPLrxKFc59M129K30S2wmwnwxmnnjTfeIDIykkGDBpGZ\nmcltt93W3F1q1UwVShcJ9q9bTn5N8hrGdBvTiD0yjJZp7ty5zJ07t7m7cdowI3kXqS0nX9HqA6sZ\n3d2cdDUMo3GZIO8idQ3ya5LXMKa7GckbhtG4TJB3kQDPAIpKisgtyq3y8bK1a9Kz0zmWd4yBHQY2\nUe8MwzhdmSDvIiJCJ79OHM45XOXjZWvXrElew5ndzsQi5u03Th+xsbGsWbOmubvRaLKysvjXv/7V\n3N2oxEQZF+rk14n0nPRatzMXQRmtWVXlhlNTU3nyyScZNmyY0/sZO3YsAElJSSxdurRBfYqJieH5\n55+v03O++eYbRo4cyaBBgxg2bBgPPPBAtdsWFRXxl7/8pcYSLKXvS2pqKldccQUAW7Zs4ZtvvqlT\nv+rKBHkXcnaGjcnHG61ZVRdBbd++nbfeeqtcqYPa/PbbbwAkJCTw4YcfurxPNdm+fTt33XUXS5Ys\nYceOHWzYsIG+fftW2q6kpAQADw8P3nvvPQYOrD4FW9qHkJAQli1bBsCmTZtYsWJFnfpWVybIu5Az\nJ18LSwrZdHATUV3NJdfG6WPNmjWO8r/R0dHcd999jBw5ktDQUNavX88ll1xC//79eeKJJxzPKR35\nPvzww6xatYrIyEgWLlyI1Wpl3rx5REVFER4e7ihwVtH/+3//jwEDBjBu3Dj+/PNPR3tcXBzTpk1j\nxIgRjB8/vtxjpZ555hkef/xx+vfvD4DFYuH2228H4MYbb+T222/nzDPP5KGHHqq0v927bfUbExIS\nGD16NEOHDuXxxx937DsxMZEhQ4ZQVFTE//3f//Hxxx8TGRnJsmXLOHbsGNOnTyc8PJzRo0ezbdu2\nhrztNqraon5sXTo1PbjyQf3Hqn9U+dhPP9le1+/Jv+vQV4c2ZbeM00hL+Pvx9/ev1BYTE6PPP/+8\nqqpGR0frww8/rKqqCxcu1C5dumhaWpoWFBRot27d9NixY+X2ExsbqxdccIFjX6+99pr+/e9/V1XV\n/Px8HTFihCYkJJQ73oYNG3TIkCGal5enmZmZ2rdvX8fxzz77bN27d6+qqq5du1bPPvvsSv0dNmyY\nbt26tcrXd+ONN+qFF16oVqtVVVUnTpzo2N/q1at14sSJqqp64YUX6gcffKCqqq+88orj9SQkJOjg\nwYNVVfXdd9/Vu+66y7Hvv/zlL/rXv/5VVVV//PFHjYiIqHT8qn7H9rYqY6q5GMqFOvl1IiWrysKa\njto1aw6sMfl4o1nIgvpXZdT5ri2VcNFFFwEwePBgBg8eTHCwbTmK3r17c+DAAYKCgk4eu8Il/CtX\nrmTbtm18+umnAGRmZrJv3z569uzp2GbVqlVceumleHt74+3t7TheTk4Oq1evduTEAQoLC+vc/yuu\nuAIRITs7m3Xr1jF79mzHYxkZGQCsXr2a5cuXA3Ddddfx0EMPVdqPnhzcArYU1eeffw7AxIkTOXr0\nKNnZ2Q1aVtEEeRfq5NeJTWmbqnysV68YAOKPx9O/ff8m7JVh2Lg6UDdEaW7eYrGUy9NbLBanlv57\n+eWXmTRpUrWPV6zvUnrbarUSFBTEpk1V/52WGjRoEBs2bGDIkCFVPl5aEtlqtRIYGMhPP/1Ua5+d\nVfFDraFMTt6FnMnJp+ek09nfrFZjnH7qG7wCAgLIyspy3J8yZQqLFy92fBjs2bOH3Nzy16eMHz+e\nL774gvz8fLKysvjqq68c++rVq5fjW4CqsnXr1krHnDdvHk8++SR79+4FbMH8tddeq7RdYGAgvXr1\ncpxItVqtjpLIY8eO5aOPPgJgyZIlVb62wMDAcq9t3Lhxjm1jY2Pp2LFjgxdHN0HehZyZQpmWnWaC\nvNGq5ebm0r17d8fPP//5T6DqGS4VywtXfAwgPDwcNzc3IiIiWLhwIbfccgthYWEMGzaMIUOGcMcd\nd1Qa/UdGRnLVVVcRHh7OeeedV662/JIlS3jrrbeIiIhg8ODBfPnll5WOPWTIEF588UVmzJhBWFgY\nQ4YMISEhoVLfSvf39ttvExERwZAhQxwfKAsXLuSVV15h6NChpKamVlmGeeLEiezcudNx4jUmJoaN\nGzcSHh7Oo48+ynvvvUdDmVLDLpSalcrw14dz8P7qV4ga+PJAPrvyMwZ1GtSEPTNOF6dCqWGjYUyp\n4WbUwbcDR3KPYFVrtduYdI1hGE3JqSAvIm4isklE/mu/HyUi6+xt60VkZJltHxGRvSKyW0Qml2kf\nLiLb7I8tdP1LaX6ebp4EeAZwPO94pccSEmLIL84npzCHIJ+gKp5tGIbhes6O5O/Btpxf6XeEZ4An\nVDUS+D/7fUQkDLgKCAOmAovlZCLqVWCWqvYD+onIVNe8hJalupOvSUkLSM9OJ9g/2NSsMQyjyTiz\nkHc34DzgTaA0YB8E2thvtwVKJ4dfDCxV1SJVTQT2AaNEpAsQoKrr7Nu9D0x3yStoYWqaYZOek06w\nX3AT98gwjNOZM/Pk/wnMAwLLtD0M/Coiz2H7oCi9uicEWFtmu2SgK1Bkv10qxd7e6tQ0w8bMrDEM\no6nVGORF5ALgkKpuEpHoMg+9BdytqstF5ArgbaD6KxPqKCYmxnE7Ojq6xspuLU1NI3kT5A3jpMWL\nF3PDDTc4FvU2nBcbG0tsbKxT29Y2kh8DXCQi5wHeQKCIfABEqeq59m0+xZbKAdsIvXuZ53fDNoJP\nsd8u21719f+UD/KnmmC/6itRpmebdI3R+lksFu677z6ee+45AJ577jlycnKYP3++Y5t///vfHDt2\nrNkC/DvvvMOiRYsA2LFjBwMHDsTNzY1p06bx5JNP1vr82bNnc9999xEaGlrtNi+++CK33XYbPj4+\nLut3qYqD3wULFlS7bY05eVV9VFW7q2ov4GrgR1WdCewTkQn2zc4G9thvfwlcLSKeItIL6AesU9U0\nIFNERtlPxM4EvqjXq2vhqhvJ9+gx34zkjdOCp6cny5cv5+jRo0DVF0FZrdZylRldyZmyCDfddBOb\nNm1i06ZNdO3aldjYWDZt2uRUgLdarbzxxhs1BniwXQxV8Urc5lDXaR6ls2tuBZ4Rkc3A3+33UdWd\nwCfYZuJ8A8wpc2XTHGwj/r3APlX9toF9b5GqC/K9esWQlmOCvNH6eXh4cOuttzqudC3rxhtv5LPP\nPuP6668HTpYTjo2NZcKECUyfPp0+ffrw8MMP88EHHxAVFcXQoUOJj48H4PDhw1x++eVERUURFRXF\n6tWrAdu3/5kzZ3LWWWdxww03kJSUxNlnn014eDjnnnsuBw4ccKrv06dPZ8SIEQwePJg33njD0e7v\n788DDzxAREQEa9asITo6mo0bNwK2gmljxoxh+PDhXHnlleTk5LBo0SJSU1OZOHEi55xzDgB33HEH\nI0eOZPDgweWyFQ8//DCDBg0iPDycefPm1fHddkJ15Smb64cWUCq1IX5J/EXHvjW2ysfGvjVWf078\nuYl7ZJxOWsLfj7+/v2ZmZmrPnj01IyNDn3vuOY2JiVFVW5neTz/9tNy2qqo//fSTtm3b1lFyOCQk\nROfPn6+qtnLEc+fOVVXVGTNm6K+//qqqqklJSRoaGqqqqvPnz9cRI0Zofn6+qqpecMEF+v7776uq\n6ttvv63Tp0+vtr89e/bUo0ePqqo6yhzn5ubq4MGDHfdFRJctW+Z4TnR0tG7cuFEPHz6s48eP19zc\nXFVVfeqppxylgsvut+y+i4uLNTo6Wrdu3apHjhzRAQMGOLbJyMio9f2t6neMKTXcdMyJV6PFquPq\nSOXUsVRCQEAA119/PYsWLXI6Jz1y5EhHyeG+ffsyZcoUwFaOuLTK4/fff8+uXbscz8nKyiInJwcR\n4aKLLnJUtFy7di1ffGHLCF933XU8+OCDTvVh4cKFjucdOHCAvXv3EhUVhZubG5dddlm5bVWVtWvX\nsnPnTsaMsa30VlhY6Lhd0ccff8wbb7xBcXExBw8eZNeuXYSFheHt7c2sWbO44IILuOCCC5zqZ12Y\nIO9iZgql0WI1cU2buXPnMmzYMG666SZHm7u7O1arreyH1WotV8u9YsnhsuWIS/Psqsrvv/+Op6dn\npeOVlv8tpXV8vbGxsfzwww+sXbsWb29vJk6cSH5+PgDe3t7VFlKbNGlSrcsTJiQk8Pzzz7Nhwwba\ntGnDTTfdRF5eHm5ubqxbt44ffviBTz/9lJdffpkffvihTv2ujbn00sXaerclryiP/OL8cu3ZhdlY\n1UqAZ0Az9cwwmlZQUBBXXnklb731liNA9uzZ05HL/vLLLykqKqrTPidPnuyYFQO2hbCrMmbMmHJl\nfsePH1/rvjMzMwkKCsLb25vdu3ezdu3aGrcXEc4880x+++034uLiANuiJKXliQMCAsjMzHTs28/P\nj8DAQNLT0/nmm28QEXJycjhx4gTTpk3jhRdeqPb1NIQJ8i4mInTy68ThnMPl2vfse5Rg/+A6Lyhs\nGKeasv/H77//fo4cOeK4P3v2bH7++WciIiJYu3ZtuVrpNZUcLn1s0aJFbNiwgfDwcAYNGlSuxnvZ\n57/00ku88847hIeHs2TJEhYurL5cVunzpk6dSnFxMWFhYTzyyCOMHj260jYVn9ehQwfeffddZsyY\nQTfSgxcAAAzySURBVHh4OGPGjHGsGXvrrbcydepUzjnnHMLDw4mMjGTgwIFce+21nHXWWYAt3XTh\nhRcSHh7OuHHjqjxZ3VCm1HAjGPbaMN648A2Ghwx3tMXGCo/EncmaWWuasWdGa2dKDTeNoUOH8t//\n/pcePXo0+bFNqeEWoLqTryYfbxinvsmTJzN06NBmCfD1YU68NoLqgry52tUwTn0rV65s7i7UiRnJ\nNwIzkjcMo6UwQb4RVDeN0gR5wzCamgnyjaCqImVrsvubdI1hGE3OBPlG0MmvE6lZqeXavkhra0by\nhmE0ORPkG8GIkBGsT11PQXGBo81c7WqcDtzc3IiMjHT8PPPMM5W2iY2N5cILL6zTfssWBDPqxsyu\naQQd/ToS1jGMX5J+YVKfSaiqY31Xw2jNfH192bRpk8v3W/aCKKNuzEi+kZzf73xW7F0BQEZBBp5u\nnvh6+NbyLMNonb799ltCQ0MZPnw4y5cvd7SvW7eOMWPGMGzYMMaOHcuePbalKfLy8rj66qsJCwvj\n0ksvJS8vz1zkVU8myDeS8/qdx9d7vwZMqsY4feTl5ZVL1yxbtoz8/HxuvfVWvvrqKzZu3EhaWppj\nVB4aGsqqVav4448/WLBgAY8++igAr776Kv7+/uzcuZMFCxawceNGM5KvJ5OuaSSRnSPJLsxm79G9\npGenM6NbQe1PMoxGJE6uCVoVdXKdZR8fn0rpms2bN9OrVy/69OkD2Er/vv766wCcOHGC66+/nn37\n9iEijmqTq1at4p577gFgyJAhDB06tN59P905FeRFxA3YACSr6oX2truwrfZUAnytqg/Z2x8Bbra3\n362qK+3tw4F3sa0Vu0JV73HtS2lZRIRpfaexYu8KOvt3ZmLQ/ubuknGaczZQu1rFEXjZtMsTTzzB\nOeecw/Lly0lMTGTixIlVbmfUn7PpmnuwLemnACIyEbgIGKqqg4Hn7O1hwFVAGDAVWCwnf8OvArNU\ntR/QT0SmuuxVtFDn9z+fr/d+TVp2WnN3xTCazYABA0hMTHQs4bd06VJH4M/MzCQkJASAd9991/Gc\n8ePHO2q0b9++na3/v737j62qPuM4/v4Exg+nrrAZ55TZsoG2a2lpO+h+NFSk01lEV2PRZAzJxAjz\nxxYYG2gCi1H5Bwbb6hJQh5jpADGdhA3HoDDJRKblh4A6a1oEF+xcYQwGAeTZH+f00lYKt6y9t5zz\nvJKb9Hzvued+z5Pw3C/fc77P2bEjtZ2OkHMmeUlXATcRPJ+1JWFPAR43sxMAZtZSV/cW4HkzO2Fm\njUA9MFLSFcAlZrYl3G8pcGuXnUUPNWbwGF7d9yrvHXgv3V1xLiXaz8nPmjWLfv36sWjRIioqKigq\nKko8/QlgxowZzJw5k8LCQj7++ONE8p8yZQqHDx8mJyeH2bNnU1xcnK5TuuCds9SwpBXAY8ClwHQz\nu1nSVuD3BKP1Y2H765J+CWw2s9+Gn32S4IHejcBcMysP20uBGS1TP+2+74IvNdza9UuvZ2fTTpYV\nN1FWFp3zcj2TlxqOvs6WGj7rnLyksUCTmW2VVNbucwPMrETSV4HlwOD/q+ettH6SeVlZGWVpmkvs\nChVDKljfsD7d3XDORciGDRvYkOSF9LOO5CU9BkwAThJcML0UeBH4HMHIfGO4Xz1QAtwNYGZzw/Y1\nwGxgD1BrZtlh+53AKDO79wzfGamR/DsfvcO11dey6TuT+cawRenujos4H8lHX5c+NMTMZpnZIDPL\nAu4A1pvZBKAGGB0efCjQx8w+Al4C7pDUR1IWMATYYmb7gUOSRoYXYluOEXlDPzuUyuxKsofMTXdX\nnHMx1Nn75Ft+Pp4Gnpb0JnAc+B6Ame2WtJzgTpyTwNRWw/KpBLdQ9ie4hXLN/9n3C4IkVlatTHc3\nnHMx5c94dS5CfLom+vwZr845dxYvv/wy27dvT3c3UsaTvHOuy3RXqeHzVVFRwaFDhxLbtbW1rF27\nlvz8/JR8f0/gtWtSpKFhDllZc9LdDee6VXeVGj5fq1evbrN93XXXtSmdEAc+kk+RPXt+lu4uOJc2\nHZUanjNnDvPmzUts5+bm8v77QZ2npUuXkp+fT0FBARMnTgRg1apVlJSUUFhYSHl5OU1NwWM2Dx8+\nzKRJkxg2bBj5+fmJ78jMzKS5uRmA+fPnk5eXR15eHgsXLgSgsbGR7Oxs7rnnHnJzc7nhhhs4duxY\n9wckhTzJO+e6TGdLDbcvXtayvWvXLh599FFqa2vZtm0bCxYsAKC0tJTNmzdTV1fH+PHjE9NBjzzy\nCAMGDGDHjh1s3749MVpvOd4bb7zBkiVL2LJlC5s3b2bx4sVs27YNgPr6eu677z527txJRkYGK1dG\n6244n65xLiY2aMN5f7bMypLar7Olhs/EzFi/fj1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      "text/plain": [
       "<matplotlib.figure.Figure at 0x110809b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Segunda Iteración: explorar a la izquierda de este primer nodo\n",
    "# definamos la región donde queremos explorar:\n",
    "ind_reg = prexmat[:,Nodes[0][0]] <= Nodes[0][1]\n",
    "# podemos hacer un copy-paste del código anterior (sólo tenemos que tener cuidado con el ind_reg)\n",
    "#--------------------------------------\n",
    "# Queremos guardar los resultados acá\n",
    "SSRMat = np.zeros((G,nvar))\n",
    "for k in range(nvar):\n",
    "    # seleccionemos la variable\n",
    "    xk    = prexmat[:,k].copy()\n",
    "    # el grid va a ser sobre los percentiles 5% y 95%\n",
    "    q05   = np.percentile(xk,5)\n",
    "    q95   = np.percentile(xk,95)\n",
    "    gridk = np.linspace(q05,q95,G)\n",
    "    # empezamos el loop sobre el grid\n",
    "    for t in range(G):\n",
    "        dum_kt = 1.0*(np.asarray(xk>gridk[t]).reshape((N,1)))\n",
    "        # para condicionar que la búsqueda sea sobre ind_reg vamos a utilizar NaNs\n",
    "        # LA FUNCION OLS_DAN ELIMINA LAS FILAS DONDE HAY NANS\n",
    "        dum_kt[ind_reg==False] = np.nan\n",
    "        xmat   = np.concatenate((np.ones((N,1)), dum_kt),axis=1)\n",
    "        olstk  = ols.ols_dan(yy, xmat)\n",
    "        # guardemos el ssr\n",
    "        SSRMat[t,k] = olstk.ssr()\n",
    "\n",
    "# guardemos el menor, y el threshold correspondiente\n",
    "ssr_min = SSRMat.min()        \n",
    "var_min = np.dot(((SSRMat==ssr_min).mean(axis=0)>0),np.arange(nvar))\n",
    "# ahora el threshold\n",
    "xk    = prexmat[:,var_min].copy()\n",
    "q05   = np.percentile(xk,5)\n",
    "q95   = np.percentile(xk,95)\n",
    "gridk = np.linspace(q05,q95,G)\n",
    "ixmin = np.argmin(SSRMat[:,var_min])\n",
    "thr_min = gridk[ixmin]\n",
    "print 'la segunda variable es: ', labs_x[var_min]\n",
    "print 'el punto de corte es: ', thr_min\n",
    "\n",
    "# grafiquémoslo\n",
    "SSRMat = pd.DataFrame(SSRMat, columns = labs_x)\n",
    "SSRMat.plot()        \n",
    "plt.legend(loc='best', fontsize=10)\n",
    "ymin, ymax = plt.ylim()\n",
    "plt.plot([ixmin, ixmin],[ymin,ymax], ls='--')\n",
    "#Actualicemos la lista donde guardamos el árbol\n",
    "Nodes.append([Nodes[0],[var_min,thr_min]])\n",
    "# Es útil guardar la región correspondiente al nodo que acabamos de explorar:\n",
    "# Las columnas corresponderán al orden de los nodos\n",
    "RegMat = np.concatenate((np.ones((N,1)),ind_reg.reshape((N,1))),axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 370,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "la tercera variable es:  Límite de Crédito\n",
      "el punto de corte es:  4663.1969697\n"
     ]
    },
    {
     "data": {
      "image/png": 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H2NvcSqFE3glpCBOvCoWtuZx9mbsX342HqwdT+01l+7ntfJXwFSfSTjDm+jFs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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110adc350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Repitamos del lado derecho\n",
    "# Segunda Iteración: explorar a la izquierda de este primer nodo\n",
    "# definamos la región donde queremos explorar:\n",
    "ind_reg = prexmat[:,Nodes[0][0]] > Nodes[0][1]\n",
    "# podemos hacer un copy-paste del código anterior (sólo tenemos que tener cuidado con el ind_reg)\n",
    "#--------------------------------------\n",
    "# Queremos guardar los resultados acá\n",
    "SSRMat = np.zeros((G,nvar))\n",
    "for k in range(nvar):\n",
    "    # seleccionemos la variable\n",
    "    xk    = prexmat[:,k].copy()\n",
    "    # el grid va a ser sobre los percentiles 5% y 95%\n",
    "    q05   = np.percentile(xk,5)\n",
    "    q95   = np.percentile(xk,95)\n",
    "    gridk = np.linspace(q05,q95,G)\n",
    "    # empezamos el loop sobre el grid\n",
    "    for t in range(G):\n",
    "        dum_kt = 1.0*(np.asarray(xk>gridk[t]).reshape((N,1)))\n",
    "        # para condicionar que la búsqueda sea sobre ind_reg vamos a utilizar NaNs\n",
    "        # LA FUNCION OLS_DAN ELIMINA LAS FILAS DONDE HAY NANS\n",
    "        dum_kt[ind_reg==False] = np.nan\n",
    "        xmat   = np.concatenate((np.ones((N,1)), dum_kt),axis=1)\n",
    "        olstk  = ols.ols_dan(yy, xmat)\n",
    "        # guardemos el ssr\n",
    "        SSRMat[t,k] = olstk.ssr()\n",
    "\n",
    "# guardemos el menor, y el threshold correspondiente\n",
    "ssr_min = SSRMat.min()        \n",
    "var_min = np.dot(((SSRMat==ssr_min).mean(axis=0)>0),np.arange(nvar))\n",
    "# ahora el threshold\n",
    "xk    = prexmat[:,var_min].copy()\n",
    "q05   = np.percentile(xk,5)\n",
    "q95   = np.percentile(xk,95)\n",
    "gridk = np.linspace(q05,q95,G)\n",
    "ixmin = np.argmin(SSRMat[:,var_min])\n",
    "thr_min = gridk[ixmin]\n",
    "print 'la tercera variable es: ', labs_x[var_min]\n",
    "print 'el punto de corte es: ', thr_min\n",
    "\n",
    "# grafiquémoslo\n",
    "SSRMat = pd.DataFrame(SSRMat, columns = labs_x)\n",
    "SSRMat.plot()        \n",
    "plt.legend(loc='best', fontsize=10)\n",
    "ymin, ymax = plt.ylim()\n",
    "plt.plot([ixmin, ixmin],[ymin,ymax], ls='--')\n",
    "#Actualicemos la lista donde guardamos el árbol\n",
    "Nodes.append([Nodes[0],[var_min,thr_min]])\n",
    "# Es útil guardar la región correspondiente al nodo que acabamos de explorar:\n",
    "# Las columnas corresponderán al orden de los nodos\n",
    "RegMat = np.concatenate((RegMat,ind_reg.reshape((N,1))),axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 371,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([], <a list of 0 Text yticklabel objects>)"
      ]
     },
     "execution_count": 371,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PXJsVS0W/PvkPbwDAEdEFAEdEFwAcEV0AcER0AcAR0QUAR0QXABwRXQBwRHQBwBHRBQBH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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e9e9350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Resumen hasta el momento\n",
    "plt.plot([-10,10],[0,0], color='k')\n",
    "plt.plot([0,0],[-0.1,0], color='k')\n",
    "plt.text(-1,0,u'límite <= 3189.5', verticalalignment='bottom', horizontalalignment='right')\n",
    "# siguiente nivel:\n",
    "plt.plot([-10,-10],[-1,0], color='k')\n",
    "plt.plot([10,10],[-1,0], color='k')\n",
    "plt.plot([-16,-4],[-1,-1], color='k')\n",
    "plt.plot([-16,-16],[-1.5,-1], color='k')\n",
    "plt.plot([-4,-4],[-1.5,-1], color='k')\n",
    "plt.plot([4,16],[-1,-1], color='k')\n",
    "plt.plot([4,4],[-1.5,-1], color='k')\n",
    "plt.plot([16,16],[-1.5,-1], color='k')\n",
    "plt.text(-10,-1,u'lím <= 2724.1', verticalalignment='bottom', horizontalalignment='right')\n",
    "plt.text(10,-1,u'lím <= 4663', verticalalignment='bottom', horizontalalignment='right')\n",
    "# axis\n",
    "plt.axis([-20,20,-3,1])\n",
    "plt.xticks([])\n",
    "plt.yticks([])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 372,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1.0000\n",
       "1    0.2675\n",
       "2    0.7325\n",
       "dtype: float64"
      ]
     },
     "execution_count": 372,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(RegMat==1).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 373,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "siguiente variable es:  Ingreso\n",
      "el punto de corte es:  23.4079025253\n"
     ]
    },
    {
     "data": {
      "image/png": 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jzaYqPx5C2zXGXCOudhduuzspFg/5vLmZ20oC1t0bMgQqMey1bOIm8iEGXrON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\nWMDdd99NWlqab/UngGnTpjF9+nRSU1O5cOGCL/hPnDiRkyd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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1109b9dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Cuarta Iteración: explorar a la izquierda del segundo nodo\n",
    "# Primero: obtengamos el padre de este nodo\n",
    "padre  = Nodes[1][-1]\n",
    "abuelo = Nodes[1][-2]\n",
    "# definamos la región donde queremos explorar:\n",
    "ind_reg = np.multiply(prexmat[:,padre[0]] <= padre[1],\n",
    "                      prexmat[:,abuelo[0]] <= abuelo[1])\n",
    "# podemos hacer un copy-paste del código anterior (sólo tenemos que tener cuidado con el ind_reg)\n",
    "#--------------------------------------\n",
    "# Queremos guardar los resultados acá\n",
    "SSRMat = np.zeros((G,nvar))\n",
    "for k in range(nvar):\n",
    "    # seleccionemos la variable\n",
    "    xk    = prexmat[:,k].copy()\n",
    "    # el grid va a ser sobre los percentiles 5% y 95%\n",
    "    q05   = np.percentile(xk,5)\n",
    "    q95   = np.percentile(xk,95)\n",
    "    gridk = np.linspace(q05,q95,G)\n",
    "    # empezamos el loop sobre el grid\n",
    "    for t in range(G):\n",
    "        dum_kt = 1.0*(np.asarray(xk>gridk[t]).reshape((N,1)))\n",
    "        # para condicionar que la búsqueda sea sobre ind_reg vamos a utilizar NaNs\n",
    "        # LA FUNCION OLS_DAN ELIMINA LAS FILAS DONDE HAY NANS\n",
    "        dum_kt[ind_reg==False] = np.nan\n",
    "        xmat   = np.concatenate((np.ones((N,1)), dum_kt),axis=1)\n",
    "        olstk  = ols.ols_dan(yy, xmat)\n",
    "        # guardemos el ssr\n",
    "        SSRMat[t,k] = olstk.ssr()\n",
    "\n",
    "# guardemos el menor, y el threshold correspondiente\n",
    "ssr_min = SSRMat.min()        \n",
    "var_min = np.dot(((SSRMat==ssr_min).mean(axis=0)>0),np.arange(nvar))\n",
    "# ahora el threshold\n",
    "xk    = prexmat[:,var_min].copy()\n",
    "q05   = np.percentile(xk,5)\n",
    "q95   = np.percentile(xk,95)\n",
    "gridk = np.linspace(q05,q95,G)\n",
    "ixmin = np.argmin(SSRMat[:,var_min])\n",
    "thr_min = gridk[ixmin]\n",
    "print 'siguiente variable es: ', labs_x[var_min]\n",
    "print 'el punto de corte es: ', thr_min\n",
    "\n",
    "# grafiquémoslo\n",
    "SSRMat = pd.DataFrame(SSRMat, columns = labs_x)\n",
    "SSRMat.plot()        \n",
    "plt.legend(loc='best', fontsize=10)\n",
    "ymin, ymax = plt.ylim()\n",
    "plt.plot([ixmin, ixmin],[ymin,ymax], ls='--')\n",
    "#Actualicemos la lista donde guardamos el árbol\n",
    "Nodes.append([Nodes[0],[var_min,thr_min]])\n",
    "# Es útil guardar la región correspondiente al nodo que acabamos de explorar:\n",
    "# Las columnas corresponderán al orden de los nodos\n",
    "RegMat = np.concatenate((RegMat,ind_reg.reshape((N,1))),axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 374,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "siguiente variable es:  Ingreso\n",
      "el punto de corte es:  26.8104282828\n"
     ]
    },
    {
     "data": {
      "image/png": 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31rWF+sNOuWs2bTKuGkPzIbK7vdw1weyTLwHuVdVBwBjgdhGJBx4CvlLVAcA3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\nWUNSUhKDBg2qkOPd/fy//vWvvPHGGyQ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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ef93bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Quinta Iteración: explorar a la derecha del segundo nodo\n",
    "# Primero: obtengamos el padre de este nodo\n",
    "padre  = Nodes[1][-1]\n",
    "abuelo = Nodes[1][-2]\n",
    "# definamos la región donde queremos explorar:\n",
    "ind_reg = np.multiply(prexmat[:,padre[0]] > padre[1],\n",
    "                      prexmat[:,abuelo[0]] <= abuelo[1])\n",
    "# podemos hacer un copy-paste del código anterior (sólo tenemos que tener cuidado con el ind_reg)\n",
    "#--------------------------------------\n",
    "# Queremos guardar los resultados acá\n",
    "SSRMat = np.zeros((G,nvar))\n",
    "for k in range(nvar):\n",
    "    # seleccionemos la variable\n",
    "    xk    = prexmat[:,k].copy()\n",
    "    # el grid va a ser sobre los percentiles 5% y 95%\n",
    "    q05   = np.percentile(xk,5)\n",
    "    q95   = np.percentile(xk,95)\n",
    "    gridk = np.linspace(q05,q95,G)\n",
    "    # empezamos el loop sobre el grid\n",
    "    for t in range(G):\n",
    "        dum_kt = 1.0*(np.asarray(xk>gridk[t]).reshape((N,1)))\n",
    "        # para condicionar que la búsqueda sea sobre ind_reg vamos a utilizar NaNs\n",
    "        # LA FUNCION OLS_DAN ELIMINA LAS FILAS DONDE HAY NANS\n",
    "        dum_kt[ind_reg==False] = np.nan\n",
    "        xmat   = np.concatenate((np.ones((N,1)), dum_kt),axis=1)\n",
    "        olstk  = ols.ols_dan(yy, xmat)\n",
    "        # guardemos el ssr\n",
    "        SSRMat[t,k] = olstk.ssr()\n",
    "\n",
    "# guardemos el menor, y el threshold correspondiente\n",
    "ssr_min = SSRMat.min()        \n",
    "var_min = np.dot(((SSRMat==ssr_min).mean(axis=0)>0),np.arange(nvar))\n",
    "# ahora el threshold\n",
    "xk    = prexmat[:,var_min].copy()\n",
    "q05   = np.percentile(xk,5)\n",
    "q95   = np.percentile(xk,95)\n",
    "gridk = np.linspace(q05,q95,G)\n",
    "ixmin = np.argmin(SSRMat[:,var_min])\n",
    "thr_min = gridk[ixmin]\n",
    "print 'siguiente variable es: ', labs_x[var_min]\n",
    "print 'el punto de corte es: ', thr_min\n",
    "\n",
    "# grafiquémoslo\n",
    "SSRMat = pd.DataFrame(SSRMat, columns = labs_x)\n",
    "SSRMat.plot()        \n",
    "plt.legend(loc='best', fontsize=10)\n",
    "ymin, ymax = plt.ylim()\n",
    "plt.plot([ixmin, ixmin],[ymin,ymax], ls='--')\n",
    "#Actualicemos la lista donde guardamos el árbol\n",
    "Nodes.append([Nodes[0],[var_min,thr_min]])\n",
    "# Es útil guardar la región correspondiente al nodo que acabamos de explorar:\n",
    "# Las columnas corresponderán al orden de los nodos\n",
    "RegMat = np.concatenate((RegMat,ind_reg.reshape((N,1))),axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 375,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "siguiente variable es:  Ingreso\n",
      "el punto de corte es:  58.5673353535\n"
     ]
    },
    {
     "data": {
      "image/png": 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HsPr1ncRlb74Z6JqULT/fyVnTqlXxIB/puWusJW/8ZUE+wk2cCK++GrwZHjMz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\nhL+BuqaVl2o4JiYGl8vleV3UVVLWpK5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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ef93bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sexta Iteración: explorar a la derecha del segundo nodo\n",
    "# Primero: obtengamos el padre de este nodo\n",
    "padre  = Nodes[2][-1]\n",
    "abuelo = Nodes[2][-2]\n",
    "# definamos la región donde queremos explorar:\n",
    "ind_reg = np.multiply(prexmat[:,padre[0]] <= padre[1],\n",
    "                      prexmat[:,abuelo[0]] > abuelo[1])\n",
    "# podemos hacer un copy-paste del código anterior (sólo tenemos que tener cuidado con el ind_reg)\n",
    "#--------------------------------------\n",
    "# Queremos guardar los resultados acá\n",
    "SSRMat = np.zeros((G,nvar))\n",
    "for k in range(nvar):\n",
    "    # seleccionemos la variable\n",
    "    xk    = prexmat[:,k].copy()\n",
    "    # el grid va a ser sobre los percentiles 5% y 95%\n",
    "    q05   = np.percentile(xk,5)\n",
    "    q95   = np.percentile(xk,95)\n",
    "    gridk = np.linspace(q05,q95,G)\n",
    "    # empezamos el loop sobre el grid\n",
    "    for t in range(G):\n",
    "        dum_kt = 1.0*(np.asarray(xk>gridk[t]).reshape((N,1)))\n",
    "        # para condicionar que la búsqueda sea sobre ind_reg vamos a utilizar NaNs\n",
    "        # LA FUNCION OLS_DAN ELIMINA LAS FILAS DONDE HAY NANS\n",
    "        dum_kt[ind_reg==False] = np.nan\n",
    "        xmat   = np.concatenate((np.ones((N,1)), dum_kt),axis=1)\n",
    "        olstk  = ols.ols_dan(yy, xmat)\n",
    "        # guardemos el ssr\n",
    "        SSRMat[t,k] = olstk.ssr()\n",
    "\n",
    "# guardemos el menor, y el threshold correspondiente\n",
    "ssr_min = SSRMat.min()        \n",
    "var_min = np.dot(((SSRMat==ssr_min).mean(axis=0)>0),np.arange(nvar))\n",
    "# ahora el threshold\n",
    "xk    = prexmat[:,var_min].copy()\n",
    "q05   = np.percentile(xk,5)\n",
    "q95   = np.percentile(xk,95)\n",
    "gridk = np.linspace(q05,q95,G)\n",
    "ixmin = np.argmin(SSRMat[:,var_min])\n",
    "thr_min = gridk[ixmin]\n",
    "print 'siguiente variable es: ', labs_x[var_min]\n",
    "print 'el punto de corte es: ', thr_min\n",
    "\n",
    "# grafiquémoslo\n",
    "SSRMat = pd.DataFrame(SSRMat, columns = labs_x)\n",
    "SSRMat.plot()        \n",
    "plt.legend(loc='best', fontsize=10)\n",
    "ymin, ymax = plt.ylim()\n",
    "plt.plot([ixmin, ixmin],[ymin,ymax], ls='--')\n",
    "#Actualicemos la lista donde guardamos el árbol\n",
    "Nodes.append([Nodes[0],[var_min,thr_min]])\n",
    "# Es útil guardar la región correspondiente al nodo que acabamos de explorar:\n",
    "# Las columnas corresponderán al orden de los nodos\n",
    "RegMat = np.concatenate((RegMat,ind_reg.reshape((N,1))),axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 376,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "siguiente variable es:  Límite de Crédito\n",
      "el punto de corte es:  5361.25606061\n"
     ]
    },
    {
     "data": {
      "image/png": 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T55Z7vdhSzIM/Psh7ie+x5s41Dh+sQQK2cDL1nceWWiKOITk9mVHzR/HSmpf4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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110b520d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Séptima Iteración: explorar a la derecha del segundo nodo\n",
    "# Primero: obtengamos el padre de este nodo\n",
    "padre  = Nodes[2][-1]\n",
    "abuelo = Nodes[2][-2]\n",
    "# definamos la región donde queremos explorar:\n",
    "ind_reg = np.multiply(prexmat[:,padre[0]]  > padre[1],\n",
    "                      prexmat[:,abuelo[0]] > abuelo[1])\n",
    "# podemos hacer un copy-paste del código anterior (sólo tenemos que tener cuidado con el ind_reg)\n",
    "#--------------------------------------\n",
    "# Queremos guardar los resultados acá\n",
    "SSRMat = np.zeros((G,nvar))\n",
    "for k in range(nvar):\n",
    "    # seleccionemos la variable\n",
    "    xk    = prexmat[:,k].copy()\n",
    "    # el grid va a ser sobre los percentiles 5% y 95%\n",
    "    q05   = np.percentile(xk,5)\n",
    "    q95   = np.percentile(xk,95)\n",
    "    gridk = np.linspace(q05,q95,G)\n",
    "    # empezamos el loop sobre el grid\n",
    "    for t in range(G):\n",
    "        dum_kt = 1.0*(np.asarray(xk>gridk[t]).reshape((N,1)))\n",
    "        # para condicionar que la búsqueda sea sobre ind_reg vamos a utilizar NaNs\n",
    "        # LA FUNCION OLS_DAN ELIMINA LAS FILAS DONDE HAY NANS\n",
    "        dum_kt[ind_reg==False] = np.nan\n",
    "        xmat   = np.concatenate((np.ones((N,1)), dum_kt),axis=1)\n",
    "        olstk  = ols.ols_dan(yy, xmat)\n",
    "        # guardemos el ssr\n",
    "        SSRMat[t,k] = olstk.ssr()\n",
    "\n",
    "# guardemos el menor, y el threshold correspondiente\n",
    "ssr_min = SSRMat.min()        \n",
    "var_min = np.dot(((SSRMat==ssr_min).mean(axis=0)>0),np.arange(nvar))\n",
    "# ahora el threshold\n",
    "xk    = prexmat[:,var_min].copy()\n",
    "q05   = np.percentile(xk,5)\n",
    "q95   = np.percentile(xk,95)\n",
    "gridk = np.linspace(q05,q95,G)\n",
    "ixmin = np.argmin(SSRMat[:,var_min])\n",
    "thr_min = gridk[ixmin]\n",
    "print 'siguiente variable es: ', labs_x[var_min]\n",
    "print 'el punto de corte es: ', thr_min\n",
    "\n",
    "# grafiquémoslo\n",
    "SSRMat = pd.DataFrame(SSRMat, columns = labs_x)\n",
    "SSRMat.plot()        \n",
    "plt.legend(loc='best', fontsize=10)\n",
    "ymin, ymax = plt.ylim()\n",
    "plt.plot([ixmin, ixmin],[ymin,ymax], ls='--')\n",
    "#Actualicemos la lista donde guardamos el árbol\n",
    "Nodes.append([Nodes[0],[var_min,thr_min]])\n",
    "# Es útil guardar la región correspondiente al nodo que acabamos de explorar:\n",
    "# Las columnas corresponderán al orden de los nodos\n",
    "RegMat = np.concatenate((RegMat,ind_reg.reshape((N,1))),axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 377,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1.0000\n",
       "1    0.2675\n",
       "2    0.7325\n",
       "3    0.1975\n",
       "4    0.0700\n",
       "5    0.2375\n",
       "6    0.4950\n",
       "dtype: float64"
      ]
     },
     "execution_count": 377,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Confirmemos que hemos venido haciendo bien los cortes\n",
    "pd.DataFrame(RegMat==1).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 378,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 3189.5166666666655],\n",
       " [[1, 3189.5166666666655], [1, 2724.1439393939386]],\n",
       " [[1, 3189.5166666666655], [1, 4663.1969696969682]],\n",
       " [[1, 3189.5166666666655], [0, 23.407902525252521]],\n",
       " [[1, 3189.5166666666655], [0, 26.810428282828276]],\n",
       " [[1, 3189.5166666666655], [0, 58.567335353535334]],\n",
       " [[1, 3189.5166666666655], [1, 5361.2560606060579]]]"
      ]
     },
     "execution_count": 378,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 379,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "siguiente variable es:  Ingreso\n",
      "el punto de corte es:  22.2737272727\n"
     ]
    },
    {
     "data": {
      "image/png": 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SWO/Ot9D/iv6M+/I0m7Lr+KGlJSDB6a/PnKF/eDhZcXEYT55ix4cLHPbtzqdkFlAppTxs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\nl6I8wTvnXIr6H73eW7m4TA8bAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110f66e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Siguiente iteración\n",
    "# Primero: obtengamos el padre de este nodo\n",
    "padre  = Nodes[3][-1]\n",
    "# definamos la región donde queremos explorar:\n",
    "ind_reg = np.multiply(prexmat[:,padre[0]]  <= padre[1],\n",
    "                      RegMat[:,3])\n",
    "# podemos hacer un copy-paste del código anterior (sólo tenemos que tener cuidado con el ind_reg)\n",
    "#--------------------------------------\n",
    "# Queremos guardar los resultados acá\n",
    "SSRMat = np.zeros((G,nvar))\n",
    "for k in range(nvar):\n",
    "    # seleccionemos la variable\n",
    "    xk    = prexmat[:,k].copy()\n",
    "    # el grid va a ser sobre los percentiles 5% y 95%\n",
    "    q05   = np.percentile(xk,5)\n",
    "    q95   = np.percentile(xk,95)\n",
    "    gridk = np.linspace(q05,q95,G)\n",
    "    # empezamos el loop sobre el grid\n",
    "    for t in range(G):\n",
    "        dum_kt = 1.0*(np.asarray(xk>gridk[t]).reshape((N,1)))\n",
    "        # para condicionar que la búsqueda sea sobre ind_reg vamos a utilizar NaNs\n",
    "        # LA FUNCION OLS_DAN ELIMINA LAS FILAS DONDE HAY NANS\n",
    "        dum_kt[ind_reg==False] = np.nan\n",
    "        xmat   = np.concatenate((np.ones((N,1)), dum_kt),axis=1)\n",
    "        olstk  = ols.ols_dan(yy, xmat)\n",
    "        # guardemos el ssr\n",
    "        SSRMat[t,k] = olstk.ssr()\n",
    "\n",
    "# guardemos el menor, y el threshold correspondiente\n",
    "ssr_min = SSRMat.min()        \n",
    "var_min = np.dot(((SSRMat==ssr_min).mean(axis=0)>0),np.arange(nvar))\n",
    "# ahora el threshold\n",
    "xk    = prexmat[:,var_min].copy()\n",
    "q05   = np.percentile(xk,5)\n",
    "q95   = np.percentile(xk,95)\n",
    "gridk = np.linspace(q05,q95,G)\n",
    "ixmin = np.argmin(SSRMat[:,var_min])\n",
    "thr_min = gridk[ixmin]\n",
    "print 'siguiente variable es: ', labs_x[var_min]\n",
    "print 'el punto de corte es: ', thr_min\n",
    "\n",
    "# grafiquémoslo\n",
    "SSRMat = pd.DataFrame(SSRMat, columns = labs_x)\n",
    "SSRMat.plot()        \n",
    "plt.legend(loc='best', fontsize=10)\n",
    "ymin, ymax = plt.ylim()\n",
    "plt.plot([ixmin, ixmin],[ymin,ymax], ls='--')\n",
    "#Actualicemos la lista donde guardamos el árbol\n",
    "Nodes.append([Nodes[0],[var_min,thr_min]])\n",
    "# Es útil guardar la región correspondiente al nodo que acabamos de explorar:\n",
    "# Las columnas corresponderán al orden de los nodos\n",
    "RegMat = np.concatenate((RegMat,ind_reg.reshape((N,1))),axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 380,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "siguiente variable es:  Edad\n",
      "el punto de corte es:  29.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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miouL6+Q43s4t0lObVpTyTCkpKSQnJ3PbbbfRs2dPJk6caF/373//m549e9K3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\nh9MgV0opD6dBrpRSHk6DXCmlPNz/B+c3Yo+/fCTjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fe07710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Siguiente iteración\n",
    "# Primero: obtengamos el padre de este nodo\n",
    "padre  = Nodes[3][-1]\n",
    "# definamos la región donde queremos explorar:\n",
    "ind_reg = np.multiply(prexmat[:,padre[0]]  > padre[1],\n",
    "                      RegMat[:,3])\n",
    "# podemos hacer un copy-paste del código anterior (sólo tenemos que tener cuidado con el ind_reg)\n",
    "#--------------------------------------\n",
    "# Queremos guardar los resultados acá\n",
    "SSRMat = np.zeros((G,nvar))\n",
    "for k in range(nvar):\n",
    "    # seleccionemos la variable\n",
    "    xk    = prexmat[:,k].copy()\n",
    "    # el grid va a ser sobre los percentiles 5% y 95%\n",
    "    q05   = np.percentile(xk,5)\n",
    "    q95   = np.percentile(xk,95)\n",
    "    gridk = np.linspace(q05,q95,G)\n",
    "    # empezamos el loop sobre el grid\n",
    "    for t in range(G):\n",
    "        dum_kt = 1.0*(np.asarray(xk>gridk[t]).reshape((N,1)))\n",
    "        # para condicionar que la búsqueda sea sobre ind_reg vamos a utilizar NaNs\n",
    "        # LA FUNCION OLS_DAN ELIMINA LAS FILAS DONDE HAY NANS\n",
    "        dum_kt[ind_reg==False] = np.nan\n",
    "        xmat   = np.concatenate((np.ones((N,1)), dum_kt),axis=1)\n",
    "        olstk  = ols.ols_dan(yy, xmat)\n",
    "        # guardemos el ssr\n",
    "        SSRMat[t,k] = olstk.ssr()\n",
    "\n",
    "# guardemos el menor, y el threshold correspondiente\n",
    "ssr_min = SSRMat.min()        \n",
    "var_min = np.dot(((SSRMat==ssr_min).mean(axis=0)>0),np.arange(nvar))\n",
    "# ahora el threshold\n",
    "xk    = prexmat[:,var_min].copy()\n",
    "q05   = np.percentile(xk,5)\n",
    "q95   = np.percentile(xk,95)\n",
    "gridk = np.linspace(q05,q95,G)\n",
    "ixmin = np.argmin(SSRMat[:,var_min])\n",
    "thr_min = gridk[ixmin]\n",
    "print 'siguiente variable es: ', labs_x[var_min]\n",
    "print 'el punto de corte es: ', thr_min\n",
    "\n",
    "# grafiquémoslo\n",
    "SSRMat = pd.DataFrame(SSRMat, columns = labs_x)\n",
    "SSRMat.plot()        \n",
    "plt.legend(loc='best', fontsize=10)\n",
    "ymin, ymax = plt.ylim()\n",
    "plt.plot([ixmin, ixmin],[ymin,ymax], ls='--')\n",
    "#Actualicemos la lista donde guardamos el árbol\n",
    "Nodes.append([Nodes[0],[var_min,thr_min]])\n",
    "# Es útil guardar la región correspondiente al nodo que acabamos de explorar:\n",
    "# Las columnas corresponderán al orden de los nodos\n",
    "RegMat = np.concatenate((RegMat,ind_reg.reshape((N,1))),axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 381,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "siguiente variable es:  Ingreso\n",
      "el punto de corte es:  15.4686757576\n"
     ]
    },
    {
     "data": {
      "image/png": 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A8IYTqZPevR21TSRtIkR7wf5Qi8gVyi/pbk+bQPuNOpI2EUII/wwTvN1XnMjI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\n8ePH8/nnn7Nnzx7AcbMHZxn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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ee6e0d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Siguiente iteración\n",
    "# Primero: obtengamos el padre de este nodo\n",
    "padre  = Nodes[4][-1]\n",
    "# definamos la región donde queremos explorar:\n",
    "ind_reg = np.multiply(prexmat[:,padre[0]]  <= padre[1],\n",
    "                      RegMat[:,4])\n",
    "# podemos hacer un copy-paste del código anterior (sólo tenemos que tener cuidado con el ind_reg)\n",
    "#--------------------------------------\n",
    "# Queremos guardar los resultados acá\n",
    "SSRMat = np.zeros((G,nvar))\n",
    "for k in range(nvar):\n",
    "    # seleccionemos la variable\n",
    "    xk    = prexmat[:,k].copy()\n",
    "    # el grid va a ser sobre los percentiles 5% y 95%\n",
    "    q05   = np.percentile(xk,5)\n",
    "    q95   = np.percentile(xk,95)\n",
    "    gridk = np.linspace(q05,q95,G)\n",
    "    # empezamos el loop sobre el grid\n",
    "    for t in range(G):\n",
    "        dum_kt = 1.0*(np.asarray(xk>gridk[t]).reshape((N,1)))\n",
    "        # para condicionar que la búsqueda sea sobre ind_reg vamos a utilizar NaNs\n",
    "        # LA FUNCION OLS_DAN ELIMINA LAS FILAS DONDE HAY NANS\n",
    "        dum_kt[ind_reg==False] = np.nan\n",
    "        xmat   = np.concatenate((np.ones((N,1)), dum_kt),axis=1)\n",
    "        olstk  = ols.ols_dan(yy, xmat)\n",
    "        # guardemos el ssr\n",
    "        SSRMat[t,k] = olstk.ssr()\n",
    "\n",
    "# guardemos el menor, y el threshold correspondiente\n",
    "ssr_min = SSRMat.min()        \n",
    "var_min = np.dot(((SSRMat==ssr_min).mean(axis=0)>0),np.arange(nvar))\n",
    "# ahora el threshold\n",
    "xk    = prexmat[:,var_min].copy()\n",
    "q05   = np.percentile(xk,5)\n",
    "q95   = np.percentile(xk,95)\n",
    "gridk = np.linspace(q05,q95,G)\n",
    "ixmin = np.argmin(SSRMat[:,var_min])\n",
    "thr_min = gridk[ixmin]\n",
    "print 'siguiente variable es: ', labs_x[var_min]\n",
    "print 'el punto de corte es: ', thr_min\n",
    "\n",
    "# grafiquémoslo\n",
    "SSRMat = pd.DataFrame(SSRMat, columns = labs_x)\n",
    "SSRMat.plot()        \n",
    "plt.legend(loc='best', fontsize=10)\n",
    "ymin, ymax = plt.ylim()\n",
    "plt.plot([ixmin, ixmin],[ymin,ymax], ls='--')\n",
    "#Actualicemos la lista donde guardamos el árbol\n",
    "Nodes.append([Nodes[0],[var_min,thr_min]])\n",
    "# Es útil guardar la región correspondiente al nodo que acabamos de explorar:\n",
    "# Las columnas corresponderán al orden de los nodos\n",
    "RegMat = np.concatenate((RegMat,ind_reg.reshape((N,1))),axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 382,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "siguiente variable es:  Educación\n",
      "el punto de corte es:  16.2828282828\n"
     ]
    },
    {
     "data": {
      "image/png": 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V8fx1oIzjBr4dItIbyFJKLXc0vQFcCHg08Fvv3epvzi5K6upJSdnLVsvBgM+J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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110ad7e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Siguiente iteración\n",
    "# Primero: obtengamos el padre de este nodo\n",
    "padre  = Nodes[4][-1]\n",
    "# definamos la región donde queremos explorar:\n",
    "ind_reg = np.multiply(prexmat[:,padre[0]]  > padre[1],\n",
    "                      RegMat[:,4])\n",
    "# podemos hacer un copy-paste del código anterior (sólo tenemos que tener cuidado con el ind_reg)\n",
    "#--------------------------------------\n",
    "# Queremos guardar los resultados acá\n",
    "SSRMat = np.zeros((G,nvar))\n",
    "for k in range(nvar):\n",
    "    # seleccionemos la variable\n",
    "    xk    = prexmat[:,k].copy()\n",
    "    # el grid va a ser sobre los percentiles 5% y 95%\n",
    "    q05   = np.percentile(xk,5)\n",
    "    q95   = np.percentile(xk,95)\n",
    "    gridk = np.linspace(q05,q95,G)\n",
    "    # empezamos el loop sobre el grid\n",
    "    for t in range(G):\n",
    "        dum_kt = 1.0*(np.asarray(xk>gridk[t]).reshape((N,1)))\n",
    "        # para condicionar que la búsqueda sea sobre ind_reg vamos a utilizar NaNs\n",
    "        # LA FUNCION OLS_DAN ELIMINA LAS FILAS DONDE HAY NANS\n",
    "        dum_kt[ind_reg==False] = np.nan\n",
    "        xmat   = np.concatenate((np.ones((N,1)), dum_kt),axis=1)\n",
    "        olstk  = ols.ols_dan(yy, xmat)\n",
    "        # guardemos el ssr\n",
    "        SSRMat[t,k] = olstk.ssr()\n",
    "\n",
    "# guardemos el menor, y el threshold correspondiente\n",
    "ssr_min = SSRMat.min()        \n",
    "var_min = np.dot(((SSRMat==ssr_min).mean(axis=0)>0),np.arange(nvar))\n",
    "# ahora el threshold\n",
    "xk    = prexmat[:,var_min].copy()\n",
    "q05   = np.percentile(xk,5)\n",
    "q95   = np.percentile(xk,95)\n",
    "gridk = np.linspace(q05,q95,G)\n",
    "ixmin = np.argmin(SSRMat[:,var_min])\n",
    "thr_min = gridk[ixmin]\n",
    "print 'siguiente variable es: ', labs_x[var_min]\n",
    "print 'el punto de corte es: ', thr_min\n",
    "\n",
    "# grafiquémoslo\n",
    "SSRMat = pd.DataFrame(SSRMat, columns = labs_x)\n",
    "SSRMat.plot()        \n",
    "plt.legend(loc='best', fontsize=10)\n",
    "ymin, ymax = plt.ylim()\n",
    "plt.plot([ixmin, ixmin],[ymin,ymax], ls='--')\n",
    "#Actualicemos la lista donde guardamos el árbol\n",
    "Nodes.append([Nodes[0],[var_min,thr_min]])\n",
    "# Es útil guardar la región correspondiente al nodo que acabamos de explorar:\n",
    "# Las columnas corresponderán al orden de los nodos\n",
    "RegMat = np.concatenate((RegMat,ind_reg.reshape((N,1))),axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 383,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "siguiente variable es:  Ingreso\n",
      "el punto de corte es:  52.8964590909\n"
     ]
    },
    {
     "data": {
      "image/png": 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02AOBnoHEBcWRFJpkbVMcalVnS+H+du349ORJiqxU4bEmsktL8XZyUptiV0EJ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\nIQcoJ+QA5YQcoJyQA5T7AIHml653j8uxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fa725d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Siguiente iteración\n",
    "# Primero: obtengamos el padre de este nodo\n",
    "padre  = Nodes[5][-1]\n",
    "# definamos la región donde queremos explorar:\n",
    "ind_reg = np.multiply(prexmat[:,padre[0]]  <= padre[1],\n",
    "                      RegMat[:,5])\n",
    "# podemos hacer un copy-paste del código anterior (sólo tenemos que tener cuidado con el ind_reg)\n",
    "#--------------------------------------\n",
    "# Queremos guardar los resultados acá\n",
    "SSRMat = np.zeros((G,nvar))\n",
    "for k in range(nvar):\n",
    "    # seleccionemos la variable\n",
    "    xk    = prexmat[:,k].copy()\n",
    "    # el grid va a ser sobre los percentiles 5% y 95%\n",
    "    q05   = np.percentile(xk,5)\n",
    "    q95   = np.percentile(xk,95)\n",
    "    gridk = np.linspace(q05,q95,G)\n",
    "    # empezamos el loop sobre el grid\n",
    "    for t in range(G):\n",
    "        dum_kt = 1.0*(np.asarray(xk>gridk[t]).reshape((N,1)))\n",
    "        # para condicionar que la búsqueda sea sobre ind_reg vamos a utilizar NaNs\n",
    "        # LA FUNCION OLS_DAN ELIMINA LAS FILAS DONDE HAY NANS\n",
    "        dum_kt[ind_reg==False] = np.nan\n",
    "        xmat   = np.concatenate((np.ones((N,1)), dum_kt),axis=1)\n",
    "        olstk  = ols.ols_dan(yy, xmat)\n",
    "        # guardemos el ssr\n",
    "        SSRMat[t,k] = olstk.ssr()\n",
    "\n",
    "# guardemos el menor, y el threshold correspondiente\n",
    "ssr_min = SSRMat.min()        \n",
    "var_min = np.dot(((SSRMat==ssr_min).mean(axis=0)>0),np.arange(nvar))\n",
    "# ahora el threshold\n",
    "xk    = prexmat[:,var_min].copy()\n",
    "q05   = np.percentile(xk,5)\n",
    "q95   = np.percentile(xk,95)\n",
    "gridk = np.linspace(q05,q95,G)\n",
    "ixmin = np.argmin(SSRMat[:,var_min])\n",
    "thr_min = gridk[ixmin]\n",
    "print 'siguiente variable es: ', labs_x[var_min]\n",
    "print 'el punto de corte es: ', thr_min\n",
    "\n",
    "# grafiquémoslo\n",
    "SSRMat = pd.DataFrame(SSRMat, columns = labs_x)\n",
    "SSRMat.plot()        \n",
    "plt.legend(loc='best', fontsize=10)\n",
    "ymin, ymax = plt.ylim()\n",
    "plt.plot([ixmin, ixmin],[ymin,ymax], ls='--')\n",
    "#Actualicemos la lista donde guardamos el árbol\n",
    "Nodes.append([Nodes[0],[var_min,thr_min]])\n",
    "# Es útil guardar la región correspondiente al nodo que acabamos de explorar:\n",
    "# Las columnas corresponderán al orden de los nodos\n",
    "RegMat = np.concatenate((RegMat,ind_reg.reshape((N,1))),axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 384,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.0\n"
     ]
    }
   ],
   "source": [
    "# Siguiente iteración\n",
    "# Primero: obtengamos el padre de este nodo\n",
    "padre  = Nodes[5][-1]\n",
    "# definamos la región donde queremos explorar:\n",
    "ind_reg = np.multiply(prexmat[:,padre[0]]  > padre[1],\n",
    "                      RegMat[:,5])\n",
    "# miremos que tenemos el mínimo de observaciones necesario\n",
    "print ind_reg.sum()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Resumen del algoritmo:\n",
    "\n",
    "* Ya vimos que el proceso es simple pero tiene una única complicación:\n",
    "\n",
    "> **Es fundamental saber en qué región estamos explorando (RegMat) y en qué nodo estamos**\n",
    "\n",
    "\n",
    "* La región, nodos y sus antescesores fueron actualizados iterativamente, explorando el árbol de arriba a abajo (naturalmente) y de izquierda a derecha (esto no es necesario, se puede hacer una exploración por ramas).\n",
    "\n",
    "\n",
    "* Un algoritmo haría esto con un loop."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# ¿Cómo funciona el algoritmo con variables categóricas?\n",
    "\n",
    "\n",
    "* Las iteraciones anteriores se hicieron con variables continuas.\n",
    "\n",
    "\n",
    "* Para cada variable $k$, se evaluaron diferentes puntos de corte $t_{kj}$, y se calcularon variables dummies $X_k \\leq t_{kj}$.\n",
    "\n",
    "\n",
    "* Pero esto no se puede hacer con variables categóricas.\n",
    "\n",
    "\n",
    "* Tomemos el caso de una variable dummy $D_i \\in \\{0,1\\}$.\n",
    "\n",
    "\n",
    "* En este caso el grid tiene sólo dos valores, así que es inmediato calcular el $SSR$:\n",
    "\n",
    "$$\n",
    "\\sum_i (y_i - c_{D=0})^2 + (y_i - c_{D=1})^2\n",
    "$$\n",
    "\n",
    "\n",
    "* O en nuestro algoritmo, corremos la regresión \n",
    "$$\n",
    "y_i = \\alpha + \\beta D_i + \\epsilon_i\n",
    "$$\n",
    "\n",
    "y guardamos el $SSR$ correspondiente.\n",
    "\n",
    "\n",
    "* En el caso de más de dos categorías incluimos todas las variables dummy correspondientes *excluyendo* la categoría de referencia."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# CART con Scikit-learn\n",
    "\n",
    "\n",
    "* Ya vimos cómo funciona el algoritmo.\n",
    "\n",
    "\n",
    "* Una ventaja que tiene usar Scikit-learn es que nos permite estimar un CART fácilmente, pero sobre todo **visualizarlo**.\n",
    "\n",
    "\n",
    "* El proceso no es inmediato: se necesita tener instalado [Graphviz](http://www.graphviz.org/).\n",
    "\n",
    "\n",
    "* Yo instalé [esta versión (Mac OS)](http://www.ryandesign.com/graphviz/) y tuve que actualizar mi [XQuartz](http://xquartz.macosforge.org/).\n",
    "\n",
    "\n",
    "* También instalé la versión de Windows.\n",
    "\n",
    "\n",
    "* Una vez instalado tienen que incluir la carpeta en el `PATH`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn import tree\n",
    "clf = tree.DecisionTreeRegressor(max_depth=3)\n",
    "clf = clf.fit(prexmat, yy)\n",
    "labs_x = np.array(['Ingreso',u'CredLim',u'NumTarjetas','Edad',u'Edu'])\n",
    "\n",
    "\n",
    "tree.export_graphviz(clf,out_file='tree.dot', feature_names=labs_x) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Graphviz\n",
    "\n",
    "* Una vez tenemos el archivo `tree.dot` necesitamos la función `dot` de Graphviz para convertirlo a `.png`:\n",
    "\n",
    "\n",
    "* Ver [la documentación oficial](http://scikit-learn.org/stable/modules/generated/sklearn.tree.export_graphviz.html).\n",
    "\n",
    "\n",
    "* Dada mi instalación de Graphviz (y que no cambié el path), tuve que hacer lo siguiente:\n",
    "\n",
    "\n",
    ">  `/usr/local/graphviz-2.14/bin/dot -Tpng tree.dot -o tree.png`\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    " ![caption](figures/tree4.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Modelos de *Clasificación*\n",
    "\n",
    "* Como su nombre lo indica, los CART sirven también para clasificar.\n",
    "\n",
    "\n",
    "* Supongamos que tenemos $K \\geq 2$ categorías.\n",
    "\n",
    "\n",
    "* Al igual que en el caso de regresión, cada nodo $m$ representa una región $R_m$ con $n_m$ observaciones.\n",
    "\n",
    "\n",
    "* Definamos la probabilidad de asignar correctamente a categoría $k$ en el nodo $m$: \n",
    "\n",
    "$$\n",
    "\\hat{p}_{mk} = \\frac{1}{n_m} \\sum_{x_i \\in R_m} I(y_{i}=k) \n",
    "$$\n",
    "\n",
    "\n",
    "* En el nodo $m$ clasificamos una observación en la categoría \n",
    "\n",
    "$$\n",
    "k(m) = \\arg \\max_{k} \\hat{p}_{km}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Métricas de ajuste o pureza\n",
    "\n",
    "\n",
    "* En regresión utilizamos el $SSR$ para seleccionar la región y el regresor correspondiente.\n",
    "\n",
    "\n",
    "* En clasificación hay tres candidatos (pero sólo se utilizan los últimos dos):\n",
    "\n",
    "\n",
    "**Error de Clasificación:**\n",
    "\n",
    "$$\n",
    "\\frac{1}{n_m} \\sum_{x_i \\in R_m} I (y_i \\neq k(m)) = 1- \\hat{p}_{mk(m)}\n",
    "$$\n",
    "\n",
    "\n",
    "**Índice de Gini** (no confundir con el coeficiente de Gini!):\n",
    "\n",
    "$$\n",
    "\\sum_k \\hat{p}_{mk}(1-\\hat{p}_{mk}) = 1 - \\sum_k \\hat{p}_{mk}^2\n",
    "$$\n",
    "\n",
    "\n",
    "**Entropía cruzada o *deviance*:**\n",
    "\n",
    "$$\n",
    "- \\sum_k \\hat{p}_{mk} \\log(\\hat{p}_{mk})\n",
    "$$\n",
    "\n",
    "\n",
    "* Intuitivamente un nodo es *puro* cuando las observaciones se clasifican en una sola categoría.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# En el caso de 2 categorías\n",
    "\n",
    "![caption](figures/purity.png)\n",
    "\n",
    "[Figura 9.3 de ESL](http://statweb.stanford.edu/~tibs/ElemStatLearn.1stEd/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Interpretación\n",
    "\n",
    "\n",
    "* El *Índice de Gini* es muy bajo cuando todos los $\\hat{p}_{mk}$ están cerca a cero o a uno.\n",
    "\n",
    "> **Por esto se considera que es una medida de la *pureza* del nodo.  \n",
    "Un valor bajo significa que se clasifican las observaciones predominantemente en una categoría.**\n",
    "\n",
    "> Se puede interpretar como la varianza en la clasificación: deseamos alta pureza y baja varianza.\n",
    "\n",
    "* La *entropía cruzada* siempre es positiva:  \n",
    "\n",
    "$$\n",
    "\\hat{p}_{mk} \\in [0,1] \\implies \\log(\\hat{p}_{mk}) <0\n",
    "$$\n",
    "\n",
    "\n",
    "> También es muy bajo cuando todos los $\\hat{p}_{mk}$ están cerca a cero o uno."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Cómo se calcula la \"impureza\" de un nodo\n",
    "\n",
    "\n",
    "* Tomemos como ejemplo el primer nodo (raíz o inicial).\n",
    "\n",
    "\n",
    "* En ese nodo no hay restricciones sobre el espacio de regresores, así que tomamos la probabilidad incondicional:\n",
    "\n",
    "\n",
    "* **Veamos el caso del Gini (la entropía es análogo)**:\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray*}\n",
    "Gini_{root} &=& 1 - \\hat{Prob}(y=1)^2 - \\hat{Prob}(y=0)^2 \\\\\n",
    "&=& 1 - \\left( \\frac{\\# \\{y_i = 1 \\}}{N}\\right)^2 - \\left( \\frac{\\# \\{y_i = 0\\}}{N}\\right)^2\n",
    "\\end{eqnarray*}\n",
    "$$\n",
    "\n",
    "\n",
    "* Si sólo tenemos observaciones con $y=1$ o $y=2$, tenemos un nodo raíz totalmente puro y el Gini es uno."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cómo seleccionamos el primer corte: variable continua\n",
    "\n",
    "\n",
    "\n",
    "* Supongamos que tenemos una candidata $X_1$ que es una variable continua que toma valores en el rango $[\\underline{x}, \\bar{x} ]$\n",
    "\n",
    "\n",
    "* Tomemos un punto de corte candidato $\\psi \\in [\\underline{x}, \\bar{x} ]$\n",
    "\n",
    "\n",
    "* Este punto de corte genera dos regiones \n",
    "$$\n",
    "R_l = X_1 \\times \\cdots \\times X_p |_{X_1 \\leq \\psi} \\\\\n",
    "R_r = X_1 \\times \\cdots \\times X_p |_{X_1 > \\psi}\n",
    "$$\n",
    "\n",
    "* Así que tenemos dos Ginis, uno para $R_l$ y otro para $R_r$:\n",
    "\n",
    "$$\n",
    "G_l = 1 - \\hat{Prob}(y=1|R_l)^2 - \\hat{Prob}(y=0|R_l)^2 \\\\\n",
    "G_r = 1 - \\hat{Prob}(y=1|R_r)^2 - \\hat{Prob}(y=0|R_r)^2 \\\\\n",
    "$$\n",
    "\n",
    "\n",
    "* El Gini asociado no es más que el *valor esperado* (condicional al nodo padre, que en este caso es la raíz)\n",
    "\n",
    "$$\n",
    "E(G) = prob(R_l)G_l + prob(R_r)G_r\n",
    "$$\n",
    "\n",
    "donde $prob(R_l)$ es la fracción de observaciones que están en $R_l$, es decir \n",
    "$$\n",
    "\\frac{\\#\\{i: x_{1i} \\leq \\psi \\}}{N}\n",
    "$$\n",
    "\n",
    "\n",
    "* El *loop* busca todos los posibles $\\phi_k$, y obtiene, para cada variable, el corte que minimiza el índice de Gini.\n",
    "\n",
    "\n",
    "* Al final seleccionamos la variable que tenga el menor Gini, y su punto de corte correspondiente."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Qué pasa en los siguientes cortes?\n",
    "\n",
    "\n",
    "\n",
    "* El proceso continua, pero hay que tener en cuenta que las probabilidades son condicionales a estar en la región actual.\n",
    "\n",
    "\n",
    "* En cada corte hay dos pasos:\n",
    "\n",
    "    * **Cálculo del Gini de cada rama**: hay que condicionar por $R_p \\cap R_{rama}$, donde $R_p$ es la región del nodo padre.\n",
    "\n",
    "    * **Cálculo de las probabilides condicionales**: \n",
    "\n",
    "\n",
    "así, en la rama izquierda del nodo $p$\n",
    "$$\n",
    "prob(R_l|R_p) = \\frac{\\#\\{i: x_{1i} \\leq \\psi \\wedge i \\in R_p\\}}{N_p}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# veamos un ejemplo\n",
    "#data  = pd.read_excel('//Users//danielvaughan//Documents//Clase CIDE//Slides//Analitica//datasets//data_tarea6.xlsx')\n",
    "data  = pd.read_excel('E:\\\\Slides\\\\Analitica\\\\datasets\\\\data_tarea6.xlsx')\n",
    "\n",
    "N  = data.shape[0]\n",
    "nobs = N\n",
    "yy    = 1*np.asarray(data.UN_MESES_SINPAGO>0).reshape((nobs,1))\n",
    "male  = 1*np.asarray(data.SEXO=='M').reshape((nobs,1))\n",
    "edad  = np.asarray(data.EDAD_CLIENTE).reshape((nobs,1))\n",
    "payr  = np.asarray(data.PAYRATIO_PROM_6M_ANTES).reshape((nobs,1))\n",
    "saldo = np.asarray(data.BALANCE_PROM_6M_ANTES).reshape((nobs,1))\n",
    "uso   = np.asarray(data.USOVECES_PROM_6M_ANTES).reshape((nobs,1))\n",
    "score = np.asarray(data.SCORE_LAST).reshape((nobs,1)).astype('float')\n",
    "score[score<0] = np.nan\n",
    "# regresores continuos\n",
    "prexmat = np.concatenate((edad, payr, saldo, uso, score,male),axis=1)\n",
    "labs_x  = np.array(['Edad','PayR','Saldo','Uso','Score','Hombre'])\n",
    "nvar = prexmat.shape[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1a1d12e8>"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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C3J9PqmTLPnX9/z568U4Du3favrvfeZe6+b1717kpU+af8dxznQ96663eHWtqpgAT62Bi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\nhBBCaCmSRQghhJYiWYQQQmjpfwfofx5USouUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1f45f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = 50\n",
    "ImpMat  = np.zeros((G,nvar))\n",
    "for k in range(nvar):\n",
    "    # seleccionemos la variable\n",
    "    xk    = prexmat[:,k].copy()\n",
    "    # miremos si es continua (ordinal) o categórica (en este caso sólo dos categorías)\n",
    "    cont_chk = pd.Series(xk).unique().shape[0]>2\n",
    "    if cont_chk==True:\n",
    "        # el grid va a ser sobre los percentiles 5% y 95%\n",
    "        q05   = np.percentile(pd.Series(xk).dropna(),5)\n",
    "        q95   = np.percentile(pd.Series(xk).dropna(),95)\n",
    "        gridk = np.linspace(q05,q95,G)\n",
    "        # empezamos el loop sobre el grid\n",
    "        for t in range(G):\n",
    "            # Definamos la región actual\n",
    "            dum_kt = (np.asarray(xk<=gridk[t])).flatten()\n",
    "            # NaNs de la región deben corresponder a las variables\n",
    "            dum_kt[np.isnan(xk)] = np.nan\n",
    "            #---------------------------------------\n",
    "            # Ahora miremos las medidas de impurity:\n",
    "            #---------------------------------------\n",
    "            # Primero: las probabilidades de caer a la izquierda o derecha \n",
    "            frac_l = (dum_kt==True).mean()\n",
    "            frac_r = (dum_kt==False).mean()\n",
    "            # Segundo: Probabilidad condicional de estar en la categoría 1 (en el corte actual)\n",
    "            p_mk_l = np.nanmean(yy[dum_kt==True])\n",
    "            p_mk_r = np.nanmean(yy[dum_kt==False])\n",
    "            # 1. Gini en cada lado del nodo\n",
    "            gini_l = 1 - p_mk_l**2 - (1-p_mk_l)**2\n",
    "            gini_r = 1 - p_mk_r**2 - (1-p_mk_r)**2\n",
    "            sum_gini    = frac_l*gini_l + frac_r*gini_r\n",
    "            ImpMat[t,k] = sum_gini\n",
    "    else:\n",
    "        # Para las variables categóricas: cada región es una categoría\n",
    "        # En este caso (hombre=1) se que los valores son 1 y cero\n",
    "        dum_kt = (xk==True)\n",
    "        dum_kt[np.isnan(xk)] = np.nan\n",
    "        # Primero: las probabilidades de caer a la izquierda o derecha \n",
    "        frac_l = (dum_kt==True).mean()\n",
    "        frac_r = (dum_kt==False).mean()\n",
    "        # Segundo: Probabilidad condicional de estar en la categoría 1 (en el corte actual)\n",
    "        p_mk_l = np.nanmean(yy[dum_kt==True])\n",
    "        p_mk_r = np.nanmean(yy[dum_kt==False])\n",
    "        # 1. Gini en cada lado del nodo\n",
    "        gini_l = 1 - p_mk_l**2 - (1-p_mk_l)**2\n",
    "        gini_r = 1 - p_mk_r**2 - (1-p_mk_r)**2\n",
    "        sum_gini    = frac_l*gini_l + frac_r*gini_r\n",
    "        ImpMat[:,k] = sum_gini\n",
    "\n",
    "pd.DataFrame(ImpMat, columns = labs_x).plot()\n",
    "plt.legend(loc='best', fontsize=11)\n",
    "plt.ylabel('Gini Impurity')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Temas Adicionales de Árboles:\n",
    "\n",
    "## 1. Qué tan grande debe ser un árbol\n",
    "\n",
    "## 2. Bagging\n",
    "\n",
    "## 3. Random Forests\n",
    "\n",
    "Estos temas son un poco más avanzados, así que los veremos un poco más superficialmente.  Quiénes estén interesados en profundizar en estos temas pueden ver las referencias del principio."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Qué tan grande debe ser un árbol\n",
    "\n",
    "\n",
    "* Arriba vimos cómo hacer crecer un árbol de regresión o de clasificación.\n",
    "\n",
    "\n",
    "* La pregunta es qué tan grande debe ser el árbol.\n",
    "\n",
    "\n",
    "* Una primer criterio es que el árbol debe crecer hasta que haya por lo menos un mínimo de observaciones en cada región.\n",
    "\n",
    "    * Por ejemplo: cada región debe tener al menos cinco observaciones.\n",
    "    \n",
    "\n",
    "* Hay que recordar que cada rama adicional *restringe* el espacio de los regresores donde exploramos.\n",
    "\n",
    "\n",
    "* Las regiones que se forman están anidadas en el sentido que la región generada por un nodo está estrictamente contenida por la región del padre de este nodo (de su antecesor).\n",
    "\n",
    "$$\n",
    "R_{p(n)} \\subset R_n\n",
    "$$\n",
    "\n",
    "* Esto garantiza que los árboles no pueden crecer indefinidamente."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Cost-complexity Pruning\n",
    "\n",
    "\n",
    "* Una vez que crecemos un árbol lo suficientemente grande podemos proceder a podarlo.\n",
    "\n",
    "\n",
    "* En la terminología de árboles de decisión esto se conoce como *poda* o **pruning**.\n",
    "\n",
    "\n",
    "* Hay varios métodos pero acá vamos a ver uno ampliamente utilizado: *cost-complexity pruning*\n",
    "\n",
    "\n",
    "* La intuición del método es sencilla:\n",
    "\n",
    "\n",
    "* A medida que crecemos un árbol, cae el sesgo pero aumenta la varianza de la estimación.\n",
    "\n",
    "    * El argumento es igual al utilizado cuando hablamos de sobreajuste polinomial.\n",
    "\n",
    "\n",
    "* Vamos a buscar una forma de penalizar nuestra función objetivo para que balancee el tradeoff entre un mayor ajuste y una mayor complejidad.\n",
    "\n",
    "\n",
    "* En el caso de regresión, crecimos árboles que minimicen el MSE, o equivalentemente, la suma de residuos al cuadrado (SSR).\n",
    "\n",
    "\n",
    "\n",
    "$$\n",
    "SSR_{\\alpha}(T) = SSR(T) + \\alpha |T|\n",
    "$$\n",
    "\n",
    "\n",
    "donde $|T|$ denota el número de *nodos terminales o finales* del árbol $T$, y $\\alpha$ es un parámetro de penalización (que buscaremos óptimamente por validación cruzada)."
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   "source": [
    "# Cómo se podan los árboles?  \n",
    "\n",
    "\n",
    "*  Cada nodo no terminal genera un subárbol:\n",
    "\n",
    "![caption](figures/pruning.png)\n",
    " \n",
    "(Tomado de [acá](http://www.uni-weimar.de/medien/webis/teaching/lecturenotes/machine-learning/unit-en-decision-trees-pruning.pdf)) \n",
    "\n",
    "\n",
    "* Así, si eliminamos un subárbol (dejando como nodo terminal el nodo inicial del subárbol) obtenemos versiones menos complejas del árbol que crecimos originalmente.\n",
    "\n",
    "\n",
    "* Se puede mostrar que para cada valor de $\\alpha$ hay un subárbol óptimo (que minimiza $SSR_{\\alpha}(T)$)."
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   "source": [
    "# Podando los árboles\n",
    "\n",
    "\n",
    "* Hay algoritmos eficientes que permiten construir una sucesión anidada de árboles óptimos para cada valor de $\\alpha$.\n",
    "\n",
    "    * Ver [acá](http://www.cs.uu.nl/docs/vakken/mdm/trees.pdf) o [acá](http://sites.stat.psu.edu/~jiali/course/stat597e/notes2/trees2.pdf), por ejemplo.\n",
    "\n",
    "\n",
    "* Aunque Scikit-learn no permite *pruning* en su versión actual, hay alternativas compatibles con este módulo.\n",
    "\n",
    "    * Ver [acá](https://github.com/sgenoud/scikit-learn/blob/4a75a4aaebd45e864e28cfca897121d1199e41d9/sklearn/tree/tree.py)\n",
    "    \n",
    "  \n",
    "* El blog [Triangle Inequality](https://triangleinequality.wordpress.com/) tiene tres entradas muy buenas de cómo construir, crecer y [podar](https://triangleinequality.wordpress.com/2013/09/01/decision-trees-part-3-pruning-your-tree/) árboles en Python."
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   "source": [
    "# Bagging: bootstrap aggregation\n",
    "\n",
    "\n",
    "* Los árboles de decisión tienen varias ventajas:\n",
    "\n",
    "    1. Permiten capturar nolinealidades que pueden ser difíciles con otros modelos.\n",
    "    2. Hacen una segmentación del espacio de regresores.\n",
    "    3. Son fáciles de presentar visualmente (si el árbol es chico).\n",
    "    \n",
    "    \n",
    "* Sin embargo, pueden ser muy sensibles a inclusión de variables o cambio de muestras:\n",
    "\n",
    "    * La razón es que los árboles simultáneamente buscan el regresor y el punto de corte para la muestra de entrenamiento.\n",
    "    \n",
    "    * Así, la estructura de un árbol puede cambiar drásticamente con muestras diferentes.\n",
    "    \n",
    "    \n",
    "* El **bootstrap aggregation**, o *bagging*, permite lidiar precisamente con esta alta varianza."
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    "# Bagging: (cont.)\n",
    "\n",
    "* La idea es simple:\n",
    "\n",
    "> Vamos a crecer $B$ árboles con **muestras de entrenamiento** diferentes (con las mismas características del bootstrapping que vimos antes).\n",
    "\n",
    "Al final, la decisión es el promedio de las decisiones que obtuvimos.\n",
    "\n",
    "* Así, por ejemplo, si en el árbol $1$, el individuo $i$ estaba en la región $R^1_k$ con $\\bar{y}_{R^1_k} = c_k$, y en el árbol $2$ en la región $R^2_l$ con promedio $c_l$, la predicción de bagging para este individuo es:\n",
    "$$\n",
    "\\hat{y}^{b}_i = \\frac{c_k + c_l}{2}\n",
    "$$\n",
    "\n",
    "\n",
    "* En el caso de un modelo de clasificación, se puede utilizar una *regla de la mayoría*: el individuo $i$ se clasifica en la categoría que tuvo más *votos*, es decir, la categoría que apareció más frecuentemente en los resultados de las $B$ clasificaciones.\n",
    "\n",
    "\n",
    "* En *bagging* no es necesario podar los árboles: lo recomendable es hacer crecer varios árboles los suficientmente grandes en cada una de las muestras de bootstrap.\n",
    "\n",
    "\n",
    "* En Scikit-learn se pueden utilizar los métodos [BaggingClassifier](http://scikit-learn.org/stable/modules/generated/sklearn.ensemble.BaggingClassifier.html) o [BaggingRegressor](http://scikit-learn.org/stable/modules/generated/sklearn.ensemble.BaggingRegressor.html)"
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    "# Random Forests: \n",
    "\n",
    "\n",
    "* Un problema de *bagging* es que las variables más importantes suelen ser seleccionadas temprano cuando se crecen árboles.\n",
    "\n",
    "\n",
    "* Así, aunque utilicemos distintas muestras de bootstrap, los correspondientes árboles suelen tener estructuras similares.\n",
    "\n",
    "\n",
    "* Para reducir aún más la varianza de la estimación se pueden crecer *bosques aleatorios* o *random forests*.\n",
    "\n",
    "\n",
    "* La idea es muy simple:\n",
    "\n",
    "    1. Se van a crecer $B$ árboles con cada muestra de boostrap como en bagging.\n",
    "    2. Para garantizar que los árboles tienen estructuras diferentes, en cada iteración seleccionamos una muestra aleatoria de los regresores candidatos en cada rama del árbol.\n",
    "    \n",
    "    \n",
    "* Scikit-learn tiene módulos de [clasificación](http://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html) y [regresión](http://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestRegressor.html) para crecer bosques aleatorios."
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