{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"Sesion_08_clasificacion.ipynb","provenance":[],"authorship_tag":"ABX9TyOSF0ywHXHUI0HqRVLJedIX"},"kernelspec":{"name":"python3","display_name":"Python 3"},"language_info":{"name":"python"}},"cells":[{"cell_type":"markdown","source":["\n","\"Open"],"metadata":{"id":"pR0ItQuLCgvj"}},{"cell_type":"markdown","source":["# Regresión Logística \n","\n","Si deseamos clasificar algún tipo de imagen, resultado en campos medicos, astrofisicos se pueden aplicar algoritmos de clasificación. En particular en esta sesión se estudia los principios basicos de regresión logística para aplicarla a los modelos de clasificación. \n","\n","Supongamos que queremos clasificar dos tipos, basado en dos características:\n","\n"],"metadata":{"id":"jtHqy2NXCf2g"}},{"cell_type":"code","source":["import matplotlib.pyplot as plt\n","from sklearn.datasets import make_classification,make_circles\n","import numpy as np"],"metadata":{"id":"oaFiKvSsETZs","executionInfo":{"status":"ok","timestamp":1643771668976,"user_tz":300,"elapsed":361,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}}},"execution_count":39,"outputs":[]},{"cell_type":"code","source":["X1, Y1 = make_classification(\n"," n_features = 2, n_redundant = 0, n_informative=1, n_clusters_per_class=1,\n"," random_state = 1, class_sep=1.2, flip_y = 0.15)\n","plt.figure()\n","plt.scatter(X1[:, 0], X1[:, 1], marker=\"o\", c=Y1, s=25, edgecolor=\"k\")\n","plt.xlabel(\"X_1\")\n","plt.ylabel(\"X_2\")"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":297},"id":"NezLToY3FZdZ","executionInfo":{"status":"ok","timestamp":1643771010284,"user_tz":300,"elapsed":875,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}},"outputId":"711533c5-298d-4a74-aa0f-751e289ba02a"},"execution_count":3,"outputs":[{"output_type":"execute_result","data":{"text/plain":["Text(0, 0.5, 'X_2')"]},"metadata":{},"execution_count":3},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":["En este caso cada color representa los objetos tipos 0 y tipo 1. Para aplicar un algoritmo de clasificación relacionaremos el valor $h_{\\theta}(X^{i})$ con la probabilidad de obtener un valor de y dado un x parametrizado por $\\theta$, $P(y|x;\\theta)$, asi : \n","\n"," $h_{\\theta}(X^{i}) = P(y|x;\\theta) $ \n","\n"," Se cumple que: $P(y=1|x;\\theta)+P(y=0|x;\\theta) = 1$\n","\n","Si tenemos muestra equiprobables, podemos definir lo siguiente para P :\n","\n","- $P<0.5$ se obtienen los objetos tipo 0 \n","- $P \\geq 0.5$ se obtienen los objetos tipo 1\n","\n","Podemos establecer un clasificador de lods sistemas basado en las probabilidades a partir de un clasificador logístico:\n","\n","\n","\\begin{equation}\n","f(z)=\\frac{1}{(1+e^{-z})}\n","\\end{equation}\n","Cuya derivada es :\n","\n","\\begin{equation}\n","f'(z)=f(z)(1-f(z))\n","\\end{equation}\n","\n"],"metadata":{"id":"zOkENAnpCZhC"}},{"cell_type":"code","source":["f = lambda x: 1/(1+np.exp(-x))\n","fp = lambda x: f(x)*(1-f(x))\n","z=np.linspace(-10, 10, 100)\n","\n","plt.figure()\n","plt.plot(z,f(z), label=\"f(z)\")\n","plt.plot(z,fp(z), label=\"Derivada de f(z)\")\n","plt.ylabel(\"f(z)\")\n","plt.xlabel(\"z\")\n","plt.grid()\n","plt.legend()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":296},"id":"UQ8hWamuJZRJ","executionInfo":{"status":"ok","timestamp":1643771011365,"user_tz":300,"elapsed":1086,"user":{"displayName":"HERNAN DAVID SALINAS 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\n","text/plain":["
"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":["- Para valores de $z< 0.0$ la regresión logistica clasica objetos tipo 0, siendo $f(z)<0.5$\n","- Para valores de $z\\geq 0.0$ la regresión logística clasica objetos tipo 1 siendo $f(z) \\geq 0.5$\n","\n","¿Cual es la probabilidad de que dado un hyperplano, los valores de un hyperlado sean objetos tipo 0 o tipo 1?\n","\n","Aplicando la regresión logistica, a las regresiones multivariadas estudiadas en la sesiones anteriores, tenemos que el argumento $z=\\Theta^{T} X$, así:\n","\n","\n","\\begin{equation}\n","h_{\\theta}(X)=\\frac{1}{(1+e^{-\\Theta^T X})}\n","\\end{equation}\n","\n","\n","- Se cumple que para los valores del hyperplano $\\Theta^T X\\geq 0.0$, $y = 1$ \n","- Se cumple que para $\\Theta^T X < 0.0$ , $y = 0$ \n","\n","\n","Las condiciones anteriores permiten definir fronteras de desicion entre los datos a clasificar. Para los datos dados arriba, se puede establecer el siguiente clasificador.\n","\n","\n","$h_\\theta(x) = g(\\theta_0+\\theta_1 x_1+\\theta_2 x_2 ) $. \n","\n","Una clasificación del dataset nos sugiere que la frontera para este dataset es: \n","\n","$\\theta_0+\\theta_1 x_1+\\theta_2 x_2 \\geq 0.0$\n","\n","Si por algun metodo encontramos que los parametros $\\Theta$ entonces podemos definir la frontera de clasifiación. Como ejemplo supongamos que encontramos los siguientes parametros $\\Theta=[3.0, -20, 1.0]$\n","\n","Ecnontrar la ecuacion de la recta y mejorar la parametrizacion\n","\n","$3-20x1+x2=0$\n","\n","$x_2= 20 x_1 - 3$"],"metadata":{"id":"WbFziZYHJuW7"}},{"cell_type":"code","source":["x1 = np.linspace(0, 0.29, 100)\n","x2 = 20*x1-3"],"metadata":{"id":"iaXdYplNhipX","executionInfo":{"status":"ok","timestamp":1643771216044,"user_tz":300,"elapsed":378,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}}},"execution_count":35,"outputs":[]},{"cell_type":"code","source":["X1, Y1 = make_classification(\n"," n_features = 2, n_redundant = 0, n_informative=1, n_clusters_per_class=1,\n"," random_state = 1, class_sep=1.2, flip_y = 0.15)\n","plt.figure()\n","plt.scatter(X1[:, 0], X1[:, 1], marker=\"o\", c=Y1, s=25, edgecolor=\"k\")\n","plt.plot(x1, x2)\n","plt.xlabel(\"X_1\")\n","plt.ylabel(\"X_2\")"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":298},"id":"TXMfwJkuPBrs","executionInfo":{"status":"ok","timestamp":1643771216551,"user_tz":300,"elapsed":11,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}},"outputId":"d51553a4-a2b6-4603-cb18-a604429a5d8e"},"execution_count":36,"outputs":[{"output_type":"execute_result","data":{"text/plain":["Text(0, 0.5, 'X_2')"]},"metadata":{},"execution_count":36},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":["Fronteras no lineal también puede ser consideradas, para ello se puede definir $\\Theta^T X$ como funcion de un polinomio, por ejemplo \n","\n","$\\Theta^T X = \\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\theta_3 x_1^2 +\\theta_4 x_1^4$\n","\n","\\begin{equation}\n","h_\\theta(X) = \\frac{1}{1+e^{\\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\theta_3 x_1^2 +\\theta_4 x_1^4}}\n","\\end{equation}\n","\n","La frontera de desición en este caso esta determinada por:\n","\n","$\\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\theta_3 x_1^2 +\\theta_4 x_1^4 \\geq 0$ \n","para obtener un clasificador con valores de y = 1.\n","\n","Para este mismo caso, supongamos que tenmos la siguiente distribución de datos, ¿Cuál es el mejor elección de parámetros $\\Theta$ que permite clasificar los datos siguientes:\n","\n","\n","\n","\n","\n"],"metadata":{"id":"lN5iivQHZoBa"}},{"cell_type":"code","source":["X, y = make_circles(\n"," n_samples=100, factor=0.5, noise=0.05, random_state=0)\n","red = y == 0\n","green = y == 1\n","f, ax = plt.subplots()\n","ax.scatter(X[red, 0], X[red, 1], c=\"r\")\n","ax.scatter(X[green, 0], X[green, 1], c=\"g\")\n","plt.axis(\"tight\")"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":282},"id":"tEAFnp7xhhd7","executionInfo":{"status":"ok","timestamp":1643771923098,"user_tz":300,"elapsed":425,"user":{"displayName":"HERNAN DAVID SALINAS 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1.1839643638442499, -1.2696420440360447, 1.185918477713659)"]},"metadata":{},"execution_count":56},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":["Analizando el conjunto de datos, se puede observar que la frontera es la de una circunferencia con centro en (0, 0) y radio de 0.7 aproxidamente, asi nuestra elección de parámetros para el polinomio ejemplicado en la celda anterior ($\\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\theta_3 x_1^2 +\\theta_4 x_1^4 \\geq 0$ ) es: \n","\n","\n","$\\Theta^T = [0.7,0, 0, 1,1 ] $ \n","\n","Reemplando tenemos que:\n","\n","$-0.7+x_1^2+x_2^2 \\geq 0$\n","\n","$x_1^2+x_2^2 \\geq 0.7$"],"metadata":{"id":"cfQVwvgnJYgA"}},{"cell_type":"code","source":["#Por motivos graficos convirtamos la ecuación anterior parametrizada\n","#por theta \n","\n","alpha = np.linspace(0, 2*np.pi)\n","x1=0.7*np.cos(alpha)\n","x2=0.7*np.sin(alpha)\n","\n","X, y = make_circles(\n"," n_samples=100, factor=0.5, noise=0.05, random_state=0)\n","red = y == 0\n","green = y == 1\n","\n","f, ax = plt.subplots(figsize=(4,4))\n","ax.scatter(X[red, 0], X[red, 1], c=\"r\")\n","ax.scatter(X[green, 0], X[green, 1], c=\"g\")\n","\n","plt.plot(x1, x2,\"b-\")\n","plt.axis(\"tight\")\n","plt.xlabel(\"X_1\")\n","plt.ylabel(\"X_2\")"],"metadata":{"id":"9WUdPhX4JYwh","colab":{"base_uri":"https://localhost:8080/","height":297},"executionInfo":{"status":"ok","timestamp":1643773227475,"user_tz":300,"elapsed":420,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}},"outputId":"d0f0ce84-e13c-498d-a159-3dc48018d2b9"},"execution_count":107,"outputs":[{"output_type":"execute_result","data":{"text/plain":["Text(0, 0.5, 'X_2')"]},"metadata":{},"execution_count":107},{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAARsAAAEHCAYAAACeOeLBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nO2deZgU1dX/v4eBgRkRkEWiCD0iaFwAIwOuGCMuwBtFRXzVCcIPFDXRBNfob1xQxIX4CuqrJEhiCDOKkegDURABE2OICGOiDEiAQVlFtjGsI8ww5/3jdENPT1WvVXWrus/neerp7urqW6e3b917zrnnEjNDURTFbZqYNkBRlNxAxUZRFE9QsVEUxRNUbBRF8QQVG0VRPKGpaQPcoH379lxUVGTaDEXJST799NMdzNwhdn9Wik1RUREqKipMm6EoOQkRrbfar8MoRVE8QcVGURRPULFRFMUTVGwURfEEFRtFUTxBxUbxD+XlQFER0KSJ3JaXm7ZIcZCsDH0rAaS8HBg9Gti/Xx6vXy+PAaCkxJxdimNoz0bxB6WlR4Qmwv79sl/JClRslPh4NbTZsCG1/UrgULFR7IkMbdavB5iPDG3cEJwuXVLbr/6dwKFio9jj5dBm/HigsLDhvsJC2R+LlyKoOIaKjWKPl0ObkhJgyhQgFAKI5HbKFGvnsPp3AolxsSGi3xHRNiJabvM8EdELRFRFRMuI6CyvbcxZUh3aZEpJCbBuHVBfL7d2USj17wQS42ID4PcABsR5fiCA7uFtNIDJHtikAKkNbbzEaxFUHMG42DDz3wBUxzlkMIA/sLAYQBsiOs4b63KcVIY2XpKuCKpT2SzMbHwDUARguc1z7wC4IOrxQgDFFseNBlABoKJLly6sZDllZcyhEDOR3JaVJT6+sJBZXMqyFRYmfp2SMgAq2OK/bLxn4xTMPIWZi5m5uEOHRkXCspdcvVon69+JoE5l4wRBbDYD6Bz1+ITwPsUPIeCgiJ06lY0TBLGZDeCmcFTqHAC7mHmLaaN8gemrtZti57SIqVPZPFZjKy83AK8D2AKgFsAmAKMA3AbgtvDzBOAlAGsBVMLCXxO79e7d2+lhqD8hauiDiGxE3pw/FLI+fyiUWbtu+FfUZ+MZsPHZGBcbN7acERu3/uzJ4pbYuSliqTiVvW4vS1CxyUZMX63dEgXTPbZkMP3Z+xg7sQmCz0axw3QejFtJf0Hwr5j2lwUQFZugk2oI2OlzuyF2fs1cjkajWymjYqNkhhtiZ7rHlgxB6H35DBUbxZ+Y7LElQ6olMYKQi+QyKjaKkg7J9r78kHjpE0icx9lFcXEx61rfii8oKhKBiSUUkh5bFkJEnzJzcex+7dlkO9qFN4s6kg+jYpPNaBfePOpIPoyKTTajuSDmCUIY3yNUbEzhxfBGu/BmKS8/Ivh5ebLPj2F8j9AVMU3g1eqPXbpYOydzsAvvObHf8aFDR3o0OSg0gPZszODV8Ea78ObQIWwjVGxM4NXwJgiZuNmKDmEbocMoE3g5vCkpUXExgQ5hG6E9GxPo8Cb70e+4ESo2JtDhTfaj33EjdLqCoiiOotMVFEUxijqIFU+pqwMOHAC++876tkkT4NhjgY4dgYIC09YqTqJi4zaRLNINGyQSkeVJXfX1wNdfA6tXA2vWyG1k++oroLY2+bZathTRiYhP5P5ppwF9+gBdu4o7JPDkyG9ExcZNvMoUNsg33wDz5wMLFgCffy4CE53LVlAAdO8O9OwJXHWVCEiLFkDz5ta3tbXAtm2ybd165HbNGmDRImDHDplTCgBt24ro9O0rt336AN/7npnPIW1y4DcSQR3EbpKFtUz27wc++kgE5v33gcpK2d++vfzpTzkFOPnkI9vxx8vQyClqa4Hly4GlS4ElS+R2+XLpUQFA587AeecBQ4YA//VfjaPPviMLfyN2DmIVGzdp0uTIZTgaoiP/jgCwZYtcgN97D/j738W3kp8P9OsHXHopcNllQK9ezopKKuzbB/zrX0fE54MPpEdUWAhccQVw3XXAwIE+9QFlyW8kGjux0WGUmwQ4i7S+Xv60v/41MGuWOHbPOAP42c9EXPr180+v4aijgAsukA2QOY9/+xvwxz8Cf/oT8MYbMny78koRnssvlyGbLwjwbyRlrBaTCvpmbJG62BUSb789cAuZbdvGPGEC80knibnt2jHfey/z6tWmLUuP2lrm+fOZb7mFuW1beU+tWzM/+CDz1q2mreOsXOwOuiKmy9j9aG6/PRBLtH70EfMNNzDn54vp/foxl5cz19SYtsw5Dh5knjePecgQ+ToKCph//nPmDRsMG5Zly/iq2LiN6XW306SyknnAADG1TRv5861YYdoq91m5knnECOamTZmbNWMeNSq4vTe/YSc2mkHsFAErKbBlC3DLLeLYXbwYePZZYPNm4PnnJY8l2/n+94FXXwWqqoBbbxUH+Pe/D1x/vUS3FOdRsXGKgBS23rcPeOwxyX2ZNg34xS+AtWuBe+5xxuFbXlmOoklFaPJYExRNKkJ5pb+Lq4dCwIsvSpT5/vuBOXOAM88EfvnLxrWvlAyx6u4EffOVz8Yn4++6OuapU5mPO05MGzqUuarK2XOULSvjwvGFjLE4vBWOL+SyZf74DJJh504ZUgHMXbsyL1hg2qIoAuLbgfpsPMCnP4b165kvuEC+7XPPZV60KL12ypaVcWhiiGkscWhiqJGIhCaGGghNZAtNDGX+JjzmL39h7t5dPrMRI5h37DBskM8vZtHYiY0m9WU5b78NjBolmbcvvQQMG5befKLyynKM/vNo7K89MrYobFaIKVdMQUkPSatv8lgTMBr/ngiE+keDl6BWUwOMGwf86lfAMceIP+v66w3NxwpQprGWmMgxamqAn/4UuOYa4KSTJMP2ppvS/6OULixtIDQAsL92P0oXHing3aW1tX/Kbr/fKSgAnnwSqKiQ//qNNwKDBwP/+Y8BYwIWgLBCxSYL+eIL4OyzgcmTgXvvlQmM3bpl1uaGXdY/6uj94/uPR2Gzhl7mwmaFGN8/2KUwe/UCPv4Y+J//kSkb55wjE0M9JSABiHgYFxsiGkBEq4ioiogesHh+BBFtJ6LPwtvNJuwMAszAK68AxcUyU3ruXBkC5Odn3nYyvZaSHiWYcsUUhFqHQCCEWocaDLNSwW9Rrbw84O67ZXb7jh0i5h984KEBqdY09uMa71aOHK82AHkA1gLoCiAfwOcATos5ZgSA/02lXWMOYoMcOsR8553iN7zkEuYtWzJvM9oh3O6Zdpw/Lt+TSJPfo1pffsl8+unMeXnML7/s4YmTDUAYdibDjw5iIjoXwFhmvjz8+EEAYOanoo4ZAaCYme9Itt1ccxDX1UmC3u9/D9x1lyToZToD28oh3KxJM7Rq3grVNdXo0roLxvcfn1avJRFFk4qwfldjZ2iodQjrxqxz/HzpsHu3+HDefVcmp06aBDT1y7Rmw85kvzqIOwHYGPV4U3hfLEOIaBkRzSSizlYNEdFoIqogoort27e7YasvOXgQuOEGEZqxY8Wv4ESpByuHcG19LVrmt0T9o/VYN2adI0JjNVxKxj+UbFtu0aqVzIa/916J8g0caMhxbIVPncmmxSYZ/gygiJl7ApgPYJrVQcw8hZmLmbm4Q4cOnhpoiv37JToyc6aIzKOPOheWTfcPnwqR3tP6XevBYKzftR6j/zwabQvaWh4fL6pl15abgpOXJz6xV18FPvxQinXt2+fa6ZKnrfXnZ9qZbFpsNgOI7qmcEN53GGbeycwHwg+nAujtkW3W+MTxtnu3XE3nzZPliO6+29n2vQhj24XTASQd1Yr0Zn7y1k8ShubdYsQIYMYMmWM2ZIj0No1RXi4/jljy840vkGdabJYC6E5EJxJRPoDrAcyOPoCIjot6eCWAlR7a15BIvdj168XtFqkX67HgfPst0L8/8I9/AK+9Jv4ap/EijG3XS6quqU4qqhXdm0n1HE5zzTUSCZw3TxInDx3y5LSNKS21rip/9NHGaxobdWkxcx0R3QFgHiQy9TtmXkFEj0M82rMB/JyIrgRQB6AaEp0yQ2lp49l5+/fLfo++yLo6YOhQYNkyyQ7+8Y/dOU/kj126sBQbdm1wxSHcpXUXS6Ho0roLSnqUWJ6rvLL8sE1NqAkOcfx/tZcJhSNHyoXg3nuBNm2kyqHn2cZ2fpnqam/tsMC4/5yZ5wCYE7Pvkaj7DwJ40Gu7DhO9zIZd5M5Dx9u99wILF4qfwC2hiWD3h3eK8f3HW06BsOs9xUbIEglNbFvRQuVWNO2ee+R//eST4jp56qnEr3EUH5cZNT2M8jexwyY7PPoiX31V5ueMGSN+gkzwQ9JcqkmAVj4eO2Lb8tKB/MQTwO23A08/DUyY4Hjz8Uk1+c9DdCJmPOzyFaIpLPRkwfiPPwYuugi48ELJDM4kpyOZSZV+xG6iZzR278Pr3J36evlJzJghfpzLLnP8FPYYXvROl3JJB7tlNgAZjHv0RW7aJFMQWraU5UrsIpvJYvfHA+TP51ayXqbY2Z1Heajn+rhDIxMz0mtq5Hurrpb1tdq3d+U0vsOvSX3+xm54FArJpWvdOteFpqYGuPpqyd+YNStzoQHiR2i8yE9JF7sI2bSrpyVMNEwllO/UELOgQKKF1dXAzTfHH4nnAio28fDB+Pe++4BPP5We8emnJ/eaRH+WRBEar/JTUiWTiZ7JhvKd9u306iW+m1mzJDSey+gwKhEGx79Llkg5gzvvFMdwMiTjj7E6JpagFryKRzLRKDd8O/X1wIABsproP/8phdWzGfXZBIy6Olk7e+tWYOVKmYuTDMn+WSJ/vHi+G79MevQSt3w7X38N9Owp16vFi50p++FX1GcTMF5+WarrTZqUvNAAyc9pKulRgnVj1qHsmrKsLHiVLm5N0zj+eGDqVPlOH300o6YCi4qND/n6a+Chh2RN6muvTe21qf5ZnCx4FTSsfFtuTtO46iopzfrcc4kzKrIRFZtYfDDR8q67ZDLfSy+lnu5u9WchENbvWm8bWYn0cpwsHeF37BzBAFwV33Hj5Pbxxx1pLlCozyaaSMZw9Pwnj5L2IsybJ87Exx8HHn44vTai/TEEauCDCELynheYLNB1113ACy8AK1Zkp7NYHcTJYLjCWX09cMYZMmN42TKgefPM2gtCxTtTmFx2Zvt2oGtXuai8+aarpzKCOoiTwXCFs3nzJPL0yCOZCw3gTQGsoGIiyS9Chw7Su5k5U3KocgUVm2gML5fx3HMStRg61Jn2sm0dJyeJ5wiOFpf2E9pj5KyRjk/gvOceyQYv9V/upGuo2ERjMGO4slKWCbnjjsxyMKL/KHsP7kV+XsPGcjmsHY1dFA5AA8fxzpqdOHioYek9JzKsW7cGHnxQerMffphRU4FBfTaxGMoYHjVKZghv3Jj+/CeTKyJkC/EmqUbjhG+npkbcgf36AX/6U0ZN+Qr12SRLSYk4gz2aaAlIlnB5OTB8eGYTLb1aESGbSdaf5cRQtKBAloN55x2p8OcJBlM7VGx8wOTJwIEDwC9+kVk76hDOnGREhECODUWHDZOcqj/+0ZHm4mO4hraKjWEOHhSx+fGPgVNOyawtdQhnjpXjOBYGO9ZDPOss4NRTgenTHWkuPvFqaHuAio1h/v53YNs2qXeSDrEO4WZNmjV4Xh3CqRHtOLYj3nOpQiS9m0WLgC+/dKxZawyndqjYGGbuXIk+9e+f+mtjU+531uwEEaFdQbucm+fkJF5PUr3xRrl1fTRjOLVDxcYwc+dKNKJly9Rfa+UQPnjooDqEHcKrSaqhEPDDH8pQytXgsOFicCo2BtmwQebHDBqU5uvVIew6VpNU3ViZYtgwYM0aKa7lGiUlMs8vFJLxWyjk6bw/4+tG5TJz58rtwIHpvT7eIm+KO8TmMkXPFs+kxzNggNwuWgT0dnOB6ZISYytjas/GIHPmyMUl3Zm/XiyRqzTEbn3yTDOKO3WS7ZNPMmrG16jYGOLAAVnZctCg9JdozeXCV6Zwc+jat6/Unc5WVGwMsWSJLM8S6T6nSy4WvjKJm7lMZ58NVFUBO3dm3JRzOJhxrGITi0fp3P/+t9yeeaYrzSsu4ebQ9eyz5dY3vRuHM45VbKLxMJ17zRqpWXPCCc6054e1u3MBq6Hr8F7DUbqwNOPPvndvGVL7RmwczjjWWd/ReFip75prpHfzxReZtxXUtbuzAac/+x49gM6dJXjgCqlUNbBbfppIJirboLO+k8HDdO6qKqBbN2facitCoiTG6c++uFiWe3GFVHvuDmccq9hE41E6N7OzYqPJfeZw+rM//nipUezKgCPVYZHDGce5KzZWjmCP0rm3bJHCSU6JTdsC6yI4mtznPk5Hp9q2lYL3e/ZkYpUNqfbcHc44zk2xsetOAp6kc1dVya0TYlNeWY49Bxv/Mps1aabJfR7gdHQqUjytujpTyyxIp+fuYDG53BSbeN1JDyr1RS4kIQcqFZQuLG1UIxcAWjVvpc5hD3A6sdJVsTE8EdP43CgiGgDgeQB5AKYy89MxzzcH8AcAvQHsBPDfzLwuo5Marutx6JDcOrG4vJ1vYGfNThRNKsKGXRu09rDLlPQoceyzdVVsIhdOAzW2gSR6NkTUiohOstjfM9OTE1EegJcADARwGoAbiOi0mMNGAfiWmbsBmAjgmUzPa7quRybE5tPY+WsiS+46ufyI4j6uig1gpMZ2hLhiQ0TXAfg3gD8R0Qoi6hP19O8dOH9fAFXM/CUzHwQwA8DgmGMGA5gWvj8TQH+idGcThTHcnUwXq/Wpdx/Y3Wi5ltgldwENhQeFiNhk4+J1iXo2/x9Ab2Y+E8D/AzCdiK4OP5fZH17oBGBj1ONN4X2WxzBzHYBdANrFNkREo4mogogqtm/fHv+shut6pIvd6glH5x/dwGdgtawsoKHwIFBQILeTJ5u1ww0S+WzymHkLADDzEiL6EYB3iKgzYPOLNgQzTwEwBZAM4oQvMFjXI13sxKK6pho77t9x+LHd2kcaCvc/kbjFPfeYtcMNEvVs9kT7a8LCcxFkaHO6A+ffDKBz1OMTwvssjyGipgBaQxzFOUeyOR1a58Ycmc5Ri/hqTnfi3+UzEonN7YgZLjHzHgADAIx04PxLAXQnohOJKB/A9QBmxxwzG8Dw8P1rAXzA2TihKwmSFRGtc2MGK59aqo75iNhkslihX4k7jGLmz2321wI4/AkS0cfMfG6qJ2fmOiK6A8A8SOj7d8y8gogeB1DBzLMB/BbiK6oCUA0RpEDTNPypHziQ2usiYlG6sDRhSNvJcKySHPHmSSX7XeSs2KRAi3RfyMxzAMyJ2fdI1P3vAAxN3zT/EUnm++qr1EuCqoj4FyfmSWWz2DiVQZyTw5p0iUxTiExbULIDJ+ZJqdgojtKxo6wTpWKTXTjhmK+ulmH2UUc5bV0CPKhQmSipz1aSiahf9EPHLMoBiKR3o2KTHUQiUMPeGoaCpgUZrUi6aRNw7LHpF8FPC48qVCbq2fyViO4PTysAABBRRyIqg0wdiDDMUatM4FHt4QhuiI2WBvUeqyWQa+pqMP2a6WkVoF+61OV1o6xwuPynHYnEpjeAkwB8RkQXE9EvACwB8DFkqgEAgJmXO2qV13hYezhCt27iIK6rc6Y9J8KuSuo4Walv1y4pFdu3b+JjHcWjiclxxYaZv2XmWwFMBbAAwH0Azmfml5jZvghp0PBI2aPp1g2orQU2bkx8bDJoaVAz2EWa1u9an7LQL10qt5FVFjzDo4nJiXw2bYjoN5B5UQMgEyHnEtHFjlphGgMlJ049VW6dWttZS4OaIV6kKdWeZWQ1zD594h/nOB5NTE40jPongDUAipn5fWYeA/HPPEFErztqiUkMlJzo0wdo1Qp47z1n2nNz8TTFHqsIVIRUe5ZLlgCnnAK0aeOUdUni0cTkRGJzITM/G55tDQBg5s+Y+TwAHzhqiUkMlJxo1gy49FJg7lxnilvrfCgzRKaG2JFsz5JZejaeD6EieFDnJpHPZlOc515x3BpTGCo5MWgQsHkzUFmZeVs6H8pZUonslfQoQai1dY3XZHuWGzcCW7cacA57iPGyoL7BQMmJyDrfc+cCPTOue6hTGZwiduG5SGQPgO3nO77/eMvF6pLtWb77rtz26xf/uCCjGcQGOf54oFcvERvFPySK7Fn1ejLtWU6fLmUlevRw/O34Bu3ZGGbQIGDCBMmxaN3a2bbLK8uTmiGuNCReZC9Rryedz7eqCvj4Y+Dppz3OHPYY7dlE8DiDOMLAgbLawvvvO9uuJvmlT7zInhv5TOXlIjIBKxyZMio2gJEM4gjnngt06iT+aCfRJL/0iRfZczqfiVmGUD/6EXDCCWk1ERhUbAAjGcQRmjYF7rgDWLDAmahUBE3yS594/hen85kWLwbWrgV+8pNMLA4GKjaA8UXrRo+WtJ5Jk5xrU5P8Uifa8Vu6sBTj+49H/aP1DSZUOp3PNH060KIFMGRIxub7HhUbwPiidW3bAsOHA2VlkmvhBE7+KXJhNnmyPi4n85n27AFmzACuukqyybMeZs66rXfv3pwSZWXMhYXMMoSWrbBQ9nvEqlVy2kcfjX9c2bIyDk0MMY0lDk0McdkyextTOTZeG4XjCxljcXgrHF+YVlt+JPIZRb+/6C00MeTauR9/XL7zxYtdO4URIPXDG/0vibNwoYLi4mKuqKhI7UXl5cbWQI5wxRWSsr5hg3StG5kYE3YFpLeS7JU1nVC43RpUodYhrBuzLuE5/YzV5xkLgVD/qPMFDnbuBLp2BS6+GHj7bcebNwoRfcrMxbH7dRgVweAayBHuugvYvt0+CJZJhCndUHg2O5qtPs9Y3PJxPfOMDKPGjXOh8XTSOEyXBVW85Uc/An7wA/kB7tvX+PlM/vjpClU2O5qT+dzcmMi6eTPw4osSgTrjDIcbTyeNwydlQRUPIZKI1Pr1wBNPNH4+kz9+ukKVzbPJE31u7QrauZJx/cQTksj52GOON51eGodPyoIqHnPhhcCIEcCzzwIrVjR8LpM/frpClc2zyePVoilsVojnBz7v+DnXrgWmTpWOw4knOt58emkcXqV+WHmNg76lHI3yGdu2Mbdty9yvH3N9fcPn0o0wZXtUKV2io1F5j+UdjkC59blcey1zQQHz11+70jxzKNQwqhrZQiFnXxMH2ESjjAuDG1vQxYaZ+ZVX5Nt59VXn2nQiFK6kT1mZfKfjxrl8klTTOBxO/VCxCRiHDjGfdx5z+/bMO3Yk/zoVFH/y5ZfMrVoxn38+c22tyycrK5NeCZHcJiMa6bzGBjux0TwbH7NsGXDWWeLDmTo18fGZ5uEo7lBXB1x0kcx9+/xziSxnM5pnE0B69gTuuQf47W+Ti0LqTG9/8tRTwKJFwOTJ2S808VCx8TnjxkmE6uabgUSdtWxOwAsqixdLiLukBLjxRg9PbKg+UzxUbHxOfj4wcybQsaNM2Nuyxf7YbE7ACyJ79ojIdO4MvPSShyc2WJ8pHio2AaBDB2DWLODbb6UUwYED1sdlcwJe0KitBW64QWa+lJU5X/I1LgbrM8VDxSYg9OoFTJsmtWp/+lPrtaaClICXSdkKv5e8qK8Xp/677wIvvwycf77HBhiuz2SLVYgq6Fs2hL7tePhhSVh4/nnTlqRPJgmGVq/FWHC7Z9r5IsxfX8/8s5/Jd/TUU4aMcDhJL1VgE/rWnk0mGHDCjR0LDB4M3H238SF42mQSNbObqb2zZmdSs9jd7hU98oj4Z+67D/jlLx1tOnkMrPCaDMbEhojaEtF8IloTvj3G5rhDRPRZeJvtuCHpCoYhJ1yTJuIDuPBCYNgw4De/cfV0AJz/g2YSNYt3TCLBcnvFieeek0mWo0ZJCQljy7IYWuE1EcaS+ohoAoBqZn6aiB4AcAwzN7oWENFeZm6ZSttJJ/VFBCPamVZYmNwXU1QkAhNLKCReQZepqQGGDhW/wIQJciV1gtgCW4O6D8K0z6c16E0QCAxGqHUorbWo7Apy5VEe6rk+bmEvu9dG22ZX7MrNQmCvvgqMHAlce62U+szLy6i5QOPHpL7BAKaF708DcJXnFmTitTfshCsoAN56C7juOuD++4GHH7Z2GqeC1ZX/1xW/bjRsYciJ0u0Z2M22PsSHEvY44s3UBuKH+d3IQ2IGJk6UPKhLL5VeZy4LTTxMik1HZo5kjXwDoKPNcS2IqIKIFhORs4KUiWAYLpIOSA7Oa69Jt/2JJ4AxYyQSki5W/pCIsNiRToZybNQsjxr/O+3ajby2XUG7Rs8lCvM7nYd08CBwyy3iP7vqKinv2bx5Wk3lBK6KDREtIKLlFtvg6OPCHmy7X3Uo3CW7EcAkIjrJ5lyjw6JUsX379uQMzEQwfOKEy8sDXnlFhOaFF+QKW1ubXlvpXuFTeV3E/zPsrWEAgOnXTEc9WyukXbslPUqw4/4dKLumLKUwv5N5SNu3A5dcIlNJHn4YePNN4KijUm4mpzDps1kF4CJm3kJExwH4KzOfkuA1vwfwDjPPjHecJz6byOsNF0mPwCxp8Y89BvTtC7z+uhTUTgU7n0bER2NHsj4Pu4miBU0LsLNmZ9rtpoIT658vXy7F6b/5Rnw111/vqImBx48+m9kAhofvDwcwK/YAIjqGiJqH77cHcD6ALxyzIFOvfaRI+vTp8njYMGPzUIgkLP7mm8CqVVLLeMaM1Nqwu/LfVnwbQq1Dch5Qo+eT7RnYhbwj7aTbbiqU9CjBujHrGi0+lyzvvCNLJh84AHz4oQpNSlgl33ixAWgHYCGANQAWAGgb3l8MYGr4/nkAKgF8Hr4dlUzbnib1+WDNqVjWrZNaOADzyJHMe/cm/9pE9XAyqZdDY8lybSYaS76vw1NTw/zQQ1LupXdv5k2bTFvkX6D1bFzCcAjcjro66ek8+SRw8snSyznzTGPmAAjuGlQffSSO4FWrgJtuklIRse465Qh+HEZlBz6dh9K0qUSoFiwAdu8Gzj5bVm6oqzNnk9MTRd3OBt61C7jtNkmg/O474L33ZH6aCk16qNhkig9C4PG4+GKpDnfppbIIXq9ewJw5mefkpIOTE0XdzgZ++23g1FMl0nf33bLSxeWXO9J07mI1tgr6lus+Gyvq65nfeou5W8DZqM0AAAr2SURBVDcxsX9/5n/9y7RV6WO3Pnema3Nv3Mh89dXyGfXqxbx0qTP25hLQiZgu4dN5KLEQAVdfLVfoF14APvvsSH3jTZtMW5c6TmcDr10L3HorcNJJwNy5wNNPA0uXAsWNPA9KuqjYOIEP1glPlvx84M47gaoqmU81Y4Y4kB96SBa7DwpOZQNXVsrXdfLJ4o8ZNQpYuVJmbDdr5oSlSgQVmxylTRuZmfzvf0uPZ/x4oFMnSRVatMiMTycVMnU2f/KJlOro2ROYPVsKy3/1lRS7CmxRch/WHW6A1dgq6Fs2F89yi8pKKfrUqpX4K04/nfnFF5n/8x/TltmTam7Onj3Mr7/OfPHF8h6POYZ57FjmnTs9MthNfOQ7hC5SZxgHFwFzk717madOZS4uPvJ7HTmS+ZNPGi8FHAT27mV+4w3mIUOYW7SQ99SpE/OvfsW8e7dp6xzEcHW+aFRsTOKjq04qVFQw33IL81FHHfmTjhjB/Nprsh65X9m3j3nmTObrrjvysXfsKD23Dz9krqszbaELEFmLDZHnptiJjWYQe4FPs4yTZfdumXM1b54kCX77rez/wQ8kf+eyy6Sod4sWZuzbskUiR0uXAkuWiM9p3z5ZleLaa6XmT79+WV5nxke/MbsMYhUbL2jSxNrjSpRZARoDHDoE/POfwPvvA/PnA//4h5S0KCiQ6RAnn3xk694d6NbNudIL9fVAdbUkKUaEZenSI6H7vDzgjDOA886TJW9++EPJpPY9TlQPyLSCgYOo2JjER1cdp9m7V2Y/z58va5OvXg1s3tzwmBNOEPHp2hVo2VJ6QM2bW9/W1QFbtwLbtjW83bpVashET7fo1g3o00dKavTpIz2twE0lcFIkfFLyRMXGJD666njB3r2Sx7N6NbBmjdyuXi2h5f37pTzDwYPx22jeXFYB7dgROPbYhvdPO02S7dq29eb9uIrdhSgvTxJ/Avj7sBObIHQyg0/kB+ODq44XtGwpQ6p4s8zr60VwvvtOxCdy26SJCMrRRxtcncBL7CbsHjokFygga34n2rNRFJPY9WwiBHCorSUmgojfM0KVzLGqZR2N6SVzHUSHUX4l1s8TWQQPyJputYIj3+Xw4TJ0isUnpUqcQHs2fiWTNa2UYFFSYl2VywdL5jqJio1f8WkFQMUlAlKqJBN0GOVXunSxdhxmUbdaiaGkJKvEJRbt2fgVnyyCpyhOoWLjV3KgW63kFjqM8jNZ3q1Wcgvt2WQDmo+jBADt2QQdzcdRAoL2bIKO5uMoAUHFJuhoPo4SEFRsgo7PV+RUlAgqNkFH83H8hTrrbVGxCTqaj+M86QpGxFm/fr2UgY0461VwBKsq6EHffLe6gkkCsoSMb8hkJQwfLadiEuha3zmIH6+0fh9mZBLdU2d9XFRsshm/hcX9KH6xZCIY6qyPi4pNNuO3K63fxM8KO2FIprq6OuvjomKTzfjtSus38bNi/HggP7/x/t27E/fA1FkfFxWbbMZvV1q/iZ8VJSWytEMstbXJ9cBKSqRAeX293KrQHMaY2BDRUCJaQUT1RNSoEnvUcQOIaBURVRHRA17aGHicvtJm6tz1m/jZUV1tvd9PPbAgYhWi8mIDcCqAUwD8FUCxzTF5ANYC6AogH8DnAE5L1LaGvl0gk5BwbDt+D8VrCDsj4LfQNzOvZOZVCQ7rC6CKmb9k5oMAZgAY7L51SiOccu4GYZgRlB5YwPC7z6YTgI1RjzeF9zWCiEYTUQURVWzfvt0T43KKIDh3nUIdva7gaj0bIloA4HsWT5Uy8ywnz8XMUwBMAWRFTCfbznnKy8VPk+XrGjVAqyQ6jqtiw8yXZNjEZgCdox6fEN6neEUkEc9KaHRooaSA34dRSwF0J6ITiSgfwPUAZhu2Kbew8tUAQF6eDi2UlDAZ+r6aiDYBOBfAu0Q0L7z/eCKaAwDMXAfgDgDzAKwE8EdmXmHK5pzEzidTX++s0Ph9zpSSMcZqEDPz2wDettj/NYBBUY/nAJjjoWlKNF4slqd1lHMCvw+jFNN4EQYOwpwpJWNUbJT4eBEGzqWweg6jS7koiXE7DKzrmucE2rNRzKMZuzmBio1iHs3YzQlUbBR/kO6cKQ2ZBwb12SjBRUPmgUJ7Nkpw0ZB5oFCxUYKLhswDhYqNElyCUGZUOYyKjRJcNGQeKFRslOCiIfNAodEoJdhokavAoD0bRVE8QcVGURRPULFRFMUTVGwURfEEFRtFUTyBZAG77IKItgOwKJBiS3sAO1wyxyuC/h7UfvM49R5CzNwhdmdWik2qEFEFM9uuNx4Egv4e1H7zuP0edBilKIonqNgoiuIJKjbCFNMGOEDQ34Pabx5X34P6bBRF8QTt2SiK4gkqNoqieEJOig0RDSWiFURUT0S2oT4iGkBEq4ioioge8NLGRBBRWyKaT0RrwrfH2Bx3iIg+C2+zvbbTwp64nykRNSeiN8LPf0JERd5baU8S9o8gou1Rn/nNJuy0g4h+R0TbiGi5zfNERC+E398yIjrLsZMzc85tAE4FcAqAvwIotjkmD8BaAF0B5AP4HMBppm2Psm8CgAfC9x8A8IzNcXtN25rKZwrgpwB+Hb5/PYA3TNudov0jAPyvaVvjvIcLAZwFYLnN84MAzAVAAM4B8IlT587Jng0zr2TmVQkO6wugipm/ZOaDAGYAGOy+dUkzGMC08P1pAK4yaEuyJPOZRr+vmQD6ExF5aGM8/P6bSAgz/w1AdZxDBgP4AwuLAbQhouOcOHdOik2SdAKwMerxpvA+v9CRmbeE738DoKPNcS2IqIKIFhORaUFK5jM9fAwz1wHYBaCdJ9YlJtnfxJDwEGQmEXX2xjTHcO13n7WV+ohoAYDvWTxVysyzvLYnHeK9h+gHzMxEZJfDEGLmzUTUFcAHRFTJzGudtlU5zJ8BvM7MB4joVkgv7WLDNvmCrBUbZr4kwyY2A4i+Kp0Q3ucZ8d4DEW0louOYeUu4m7vNpo3N4dsvieivAH4A8TuYIJnPNHLMJiJqCqA1gJ3emJeQhPYzc7StUyG+tSDh2u9eh1H2LAXQnYhOJKJ8iLPSeDQnitkAhofvDwfQqLdGRMcQUfPw/fYAzgfwhWcWNiaZzzT6fV0L4AMOey59QEL7Y/wbVwJY6aF9TjAbwE3hqNQ5AHZFDdczw7R33JBH/mrIWPQAgK0A5oX3Hw9gToxnfjWkJ1Bq2u6Y99AOwEIAawAsANA2vL8YwNTw/fMAVEKiJpUARvnA7kafKYDHAVwZvt8CwJsAqgAsAdDVtM0p2v8UgBXhz/wvAL5v2uYY+18HsAVAbfg/MArAbQBuCz9PAF4Kv79K2ERr09l0uoKiKJ6gwyhFUTxBxUZRFE9QsVEUxRNUbBRF8QQVG0VRPEHFRlEUT1CxUTyFiDoT0VdE1Db8+Jjw4yKb498jov8Q0Tte2qk4j4qN4inMvBHAZABPh3c9DWAKM6+zecmvAAzzwDTFZVRsFBNMBHAOEY0BcAGAZ+0OZOaFAPZ4ZZjiHlk7EVPxL8xcS0T3AXgPwGXMXGvaJsV9tGejmGIgZI7OGaYNUbxBxUbxHCI6E8ClkLKTdzlVCU7xNyo2iqeES3xOBjCGmTdAHMC2Phsle1CxUbzmFgAbmHl++PHLAE4loh9aHUxEH0FKTvQnok1EdLlHdioOoyUmFEXxBO3ZKIriCRr6VoxDRD0ATI/ZfYCZzzZhj+IOOoxSFMUTdBilKIonqNgoiuIJKjaKoniCio2iKJ7wfyPne1y8ltuqAAAAAElFTkSuQmCC\n","text/plain":["
"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":["De forma general, ¿Cómo pueden ser elegidos los valores de $\\Theta$?.\n","\n","\n","\n","Para todo el conjunto de datos, tenemos que:\n","\n","Sea $\\Theta^T = [\\theta_0,\\theta_1,\\theta_2,...,\\theta_n]$ una matrix $1 \\times (n+1)$ y \n","\n","\n","\\begin{equation}\n","X =\n","\\begin{bmatrix}\n","1& 1 & 1 & .&.&.&1\\\\\n","x_1^{(1)}&x_1^{(2)} & x_1^{(3)} & .&.&.&x_1^{(m)}\\\\\n",".&. & . &.&.&.& .\\\\\n",".&. & . & .&.&.&.\\\\\n",".&. & . & .&.&.&.\\\\\n","x_n^{(1)}&x_n^{(2)} & x_n^{(3)} & .&.&.&x_n^{(m)}\\\\\n","\\end{bmatrix}_{(n+1) \\times m}\n","\\end{equation}\n","\n","\n","\\begin{equation}\n","h_\\theta (x)= \\frac{1}{1+e^{\\Theta ^T X}}\n","\\end{equation}\n","\n","\n","\n","Para ello, podemos definir la función de coste como :\n","\n","$ J (\\Theta) =\\frac{1}{m} \\sum_{i=1}^{m} \\left[-y\\log (h_{\\theta}(X ^ {i})) - (1-y)\\log (1-h_{\\theta}(X^{i})) \\right]$\n","\n","Esta función de coste permite establecer el mejor clasificadose para la regresión logistica de acuerdo a la teroria de probabilidad. Se garantiza que cuando $P(y=1|x,\\theta)$ se cumple la función de coste se minimiza, penalizando los valores que sean iguales a $P(y=0|x,\\theta)$, analogamente, se cumple que cuando $P(y=0|x,\\theta)$ se cumple la función de coste se minimiza, penalizando los valores que sean iguales a $P(y=1|x,\\theta)$. \n","La metrica empleada para la regresión lineal no es recomedada en este caso, dado que la funcion de coste puede presentar múltiples minimos que dificultan la minimizacion a través de algunas de las técnicas empleadas. Una justificación adicional para la métrica es dada mas adelante segun la teoria de la probabilidad.\n","\n","Se deja como tarea motrar que:\n","\n","\\begin{equation}\n","\\frac{\\partial J(\\theta)}{\\partial \\theta_j} = \\frac{1}{m}\\sum_{i=1}^{m}[y^{(i)}-h_\\theta X^{(i)}] X_j^{(i)}\n","\\end{equation}\n","\n","Para la demostración, muestre que:\n","- $f(z)=\\frac{1}{1+e^{-z}} = f(z)(1-f(z))$\n","- $\\frac{\\partial h_{\\theta}}{\\partial \\theta_j } = h_{\\theta}(X^{(i)})(1-h_{\\theta}(X^{(i)}))X_j^{(i)}$\n","\n","\n","La derivada permite aplicar el gradiente descendente para minimizar nuestra función de coste asi, nuestro algoritmo de minimizacion permite encontrar los valores de $\\theta$ despues de un conjunto determinado de itereaciones.\n","\n","$\\theta_j: \\theta_j - \\alpha \\frac{\\partial J}{\\partial \\theta_j}$\n","\n","\n","Otros metodos de minizacion podrian ser aplicados, tales como:\n","\n","\n","[Gradiente conjugado ](https://es.wikipedia.org/wiki/M%C3%A9todo_del_gradiente_conjugado#:~:text=En%20matem%C3%A1tica%2C%20el%20m%C3%A9todo%20del,son%20sim%C3%A9tricas%20y%20definidas%20positivas.&text=Varios%20m%C3%A9todos%20del%20gradiente%20conjugado,de%20las%20ecuaciones%20no%20lineales)\n","\n","[BFGS](https://en.wikipedia.org/wiki/Broyden%E2%80%93Fletcher%E2%80%93Goldfarb%E2%80%93Shanno_algorithm)\n","\n","\n","[L-BGFS](https://en.wikipedia.org/wiki/Limited-memory_BFGS)\n","\n","[Newton-Rhapson](https://en.wikipedia.org/wiki/Newton%27s_method)\n"],"metadata":{"id":"q7Z5BnNqhWyG"}},{"cell_type":"markdown","source":["# Interpretación estadística\n","\n","\n","¿Qué tan adeacuado es la elección de $J(\\theta)$ para el modelo de regresion logistica?\n","\n","\n","\n","\\begin{equation}\n","P(y=1|x;\\theta)= h_{\\theta}(X^{(i)})\n","\\end{equation}\n","\n","\\begin{equation}\n","P(y=0|x;\\theta)= 1-h_{\\theta}(X^{(i)}) \n","\\end{equation}\n","\n","\n","\n","\\begin{equation}\n","P(y|x;\\theta)=[h_{\\theta}(X^{(i)})]^{y}[1-h_{\\theta}(X^{(i)})]^{1-y}\n","\\end{equation}\n","\n","Asumiendo que los datos de entrenamiento son independientes:\n","\n","$\\cal{L}(\\theta)=p(\\vec{y}|x, \\theta)$\n","\n","\\begin{equation}\n","\\cal{L}(\\theta)=\\prod_{i=1}^{m} [h_{\\theta}(X^{(i)})]^{y}[1-h_{\\theta}(X^{(i)})]^{1-y}\n","\\end{equation}\n","\n","tomando el logaritmo:\n","\n","\n","\\begin{equation}\n","\\log \\cal{L}(\\theta)= \\sum_{i=1}^{m} y \\log h_{\\theta}(X^{(i)}) + (1-y)(1-h_{\\theta}(X^{(i)}))\n","\\end{equation}\n","\n","Los datos a considerar son los mas probables es decir que para encontrar los valores de $\\theta$ que nos garantizan la maxima probabilidad es necesario maximar la función anterior. Despues de realizar los calculos se puede mostrar la ecuación dada para el gradiente de la función de coste.\n","\n"],"metadata":{"id":"uIfQB4ZioV62"}},{"cell_type":"markdown","source":["En conclusión se cumple que:\n","\n","Para todo el conjunto de datos, tenemos que:\n","\n","Sea $\\Theta^T = [\\theta_0,\\theta_1,\\theta_2,...,\\theta_n]$ una matrix $1 \\times (n+1)$ y \n","\n","\n","\\begin{equation}\n","X =\n","\\begin{bmatrix}\n","1& 1 & 1 & .&.&.&1\\\\\n","x_1^{(1)}&x_1^{(2)} & x_1^{(3)} & .&.&.&x_1^{(m)}\\\\\n",".&. & . &.&.&.& .\\\\\n",".&. & . & .&.&.&.\\\\\n",".&. & . & .&.&.&.\\\\\n","x_n^{(1)}&x_n^{(2)} & x_n^{(3)} & .&.&.&x_n^{(m)}\\\\\n","\\end{bmatrix}_{(n+1) \\times m}\n","\\end{equation}\n","\n","\n","\\begin{equation}\n","h_\\theta (x)= \\frac{1}{1+e^{\\Theta ^T X}}\n","\\end{equation}\n","\n","\n","\n","- Función de coste\n","$ J (\\Theta) =\\frac{1}{m} \\sum_{i=1}^{m} \\left[-y\\log (h_{\\theta}(X ^ {i})) - (1-y)\\log (1-h_{\\theta}(X^{i})) \\right]$\n","\n","- Derivada de la funcion de coste\n","\\begin{equation}\n","\\frac{\\partial J(\\theta)}{\\partial \\theta_j} = \\frac{1}{m}\\sum_{i=1}^{m}[y^{(i)}-h_\\theta X^{(i)}] X_j^{(i)}\n","\\end{equation}\n","\n","\n","\n"],"metadata":{"id":"E31MSBuFq37Z"}},{"cell_type":"markdown","source":["Tomar el [iris dataset](https://en.wikipedia.org/wiki/Iris_flower_data_set) desde sklearn:\n","\n","```\n","from sklearn import datasets\n","\n","iris = datasets.load_iris()\n","```\n","- Realizar la clasifición de las tres clases a traves de una regresión logística y realizar multiclasicación, para ello considere lo siguiente:\n","\n","Si en un dataset existen más de 2 clases, $y={0, 1, 2, 3, ...}$ se debe construir una multiclasificación, una contra todos, la estrategia sugerida es la siguiente.\n","\n","Sea A, B, C las tres clases. Para estos valores definir:\n","\n","1. Definir la clase A como la clase 0 y todas las otras B, C como la clase 1\n","2. Encontrar el valor $h_\\theta(X) = P(y=A|x;\\theta)$\n","3. Definir la clase B como la clase 0 y todas las otras A, C como la clase 1\n","4. Encontrar el valor $h_\\theta(X) = P(y=B|x;\\theta)$\n","5. Definir la clase C como la clase 0 y todas las otras A, B como la clase 1\n","6. Encontrar el valor $h_\\theta(X) = P(y=C|x;\\theta)$\n","\n","\n"],"metadata":{"id":"Yky7THIKrS30"}},{"cell_type":"code","source":["from sklearn import datasets\n","from sklearn.model_selection import StratifiedShuffleSplit\n","import pandas as pd\n","from sklearn.linear_model import LogisticRegression\n","import matplotlib.pylab as plt\n","\n"],"metadata":{"id":"egtz5kFfHsaG","executionInfo":{"status":"ok","timestamp":1643822857020,"user_tz":300,"elapsed":771,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}}},"execution_count":239,"outputs":[]},{"cell_type":"code","source":["iris = datasets.load_iris()\n","iris.keys()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"xqXXLpeBHuzr","executionInfo":{"status":"ok","timestamp":1643828258365,"user_tz":300,"elapsed":359,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}},"outputId":"c0b5e3eb-9292-4221-900c-4bdb05ca0554"},"execution_count":320,"outputs":[{"output_type":"execute_result","data":{"text/plain":["dict_keys(['data', 'target', 'frame', 'target_names', 'DESCR', 'feature_names', 'filename', 'data_module'])"]},"metadata":{},"execution_count":320}]},{"cell_type":"code","source":["print(iris.DESCR)\n"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"MEQ4IwagzJQq","executionInfo":{"status":"ok","timestamp":1643828258735,"user_tz":300,"elapsed":3,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}},"outputId":"69316eb6-5102-446f-b1f0-3a614223b651"},"execution_count":321,"outputs":[{"output_type":"stream","name":"stdout","text":[".. _iris_dataset:\n","\n","Iris plants dataset\n","--------------------\n","\n","**Data Set Characteristics:**\n","\n"," :Number of Instances: 150 (50 in each of three classes)\n"," :Number of Attributes: 4 numeric, predictive attributes and the class\n"," :Attribute Information:\n"," - sepal length in cm\n"," - sepal width in cm\n"," - petal length in cm\n"," - petal width in cm\n"," - class:\n"," - Iris-Setosa\n"," - Iris-Versicolour\n"," - Iris-Virginica\n"," \n"," :Summary Statistics:\n","\n"," ============== ==== ==== ======= ===== ====================\n"," Min Max Mean SD Class Correlation\n"," ============== ==== ==== ======= ===== ====================\n"," sepal length: 4.3 7.9 5.84 0.83 0.7826\n"," sepal width: 2.0 4.4 3.05 0.43 -0.4194\n"," petal length: 1.0 6.9 3.76 1.76 0.9490 (high!)\n"," petal width: 0.1 2.5 1.20 0.76 0.9565 (high!)\n"," ============== ==== ==== ======= ===== ====================\n","\n"," :Missing Attribute Values: None\n"," :Class Distribution: 33.3% for each of 3 classes.\n"," :Creator: R.A. Fisher\n"," :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n"," :Date: July, 1988\n","\n","The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken\n","from Fisher's paper. Note that it's the same as in R, but not as in the UCI\n","Machine Learning Repository, which has two wrong data points.\n","\n","This is perhaps the best known database to be found in the\n","pattern recognition literature. Fisher's paper is a classic in the field and\n","is referenced frequently to this day. (See Duda & Hart, for example.) The\n","data set contains 3 classes of 50 instances each, where each class refers to a\n","type of iris plant. One class is linearly separable from the other 2; the\n","latter are NOT linearly separable from each other.\n","\n",".. topic:: References\n","\n"," - Fisher, R.A. \"The use of multiple measurements in taxonomic problems\"\n"," Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n"," Mathematical Statistics\" (John Wiley, NY, 1950).\n"," - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.\n"," (Q327.D83) John Wiley & Sons. ISBN 0-471-22361-1. See page 218.\n"," - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n"," Structure and Classification Rule for Recognition in Partially Exposed\n"," Environments\". IEEE Transactions on Pattern Analysis and Machine\n"," Intelligence, Vol. PAMI-2, No. 1, 67-71.\n"," - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\". IEEE Transactions\n"," on Information Theory, May 1972, 431-433.\n"," - See also: 1988 MLC Proceedings, 54-64. Cheeseman et al\"s AUTOCLASS II\n"," conceptual clustering system finds 3 classes in the data.\n"," - Many, many more ...\n"]}]},{"cell_type":"code","source":["iris.target_names"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"WTGnqBv5WSNk","executionInfo":{"status":"ok","timestamp":1643822860787,"user_tz":300,"elapsed":1,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}},"outputId":"4e568074-ee36-4719-92ae-9eeb6dadbb3b"},"execution_count":241,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array(['setosa', 'versicolor', 'virginica'], dtype='\n","
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sepal length (cm)sepal width (cm)petal length (cm)petal width (cm)
05.13.51.40.2
14.93.01.40.2
24.73.21.30.2
34.63.11.50.2
45.03.61.40.2
...............
1456.73.05.22.3
1466.32.55.01.9
1476.53.05.22.0
1486.23.45.42.3
1495.93.05.11.8
\n","

150 rows × 4 columns

\n","
\n"," \n"," \n"," \n","\n"," \n","
\n"," \n"," "],"text/plain":[" sepal length (cm) sepal width (cm) petal length (cm) petal width (cm)\n","0 5.1 3.5 1.4 0.2\n","1 4.9 3.0 1.4 0.2\n","2 4.7 3.2 1.3 0.2\n","3 4.6 3.1 1.5 0.2\n","4 5.0 3.6 1.4 0.2\n",".. ... ... ... ...\n","145 6.7 3.0 5.2 2.3\n","146 6.3 2.5 5.0 1.9\n","147 6.5 3.0 5.2 2.0\n","148 6.2 3.4 5.4 2.3\n","149 5.9 3.0 5.1 1.8\n","\n","[150 rows x 4 columns]"]},"metadata":{},"execution_count":243}]},{"cell_type":"code","source":["columns_name =[ \"\".join([c.capitalize() for c in cols.split()]) for cols in df.columns ]\n","columns_name =[col.replace(\"(\" ,\"_\") for col in columns_name ] \n","cols= [col.replace(\")\" ,\"\") for col in columns_name ] "],"metadata":{"id":"RxcIxZQVJpS1","executionInfo":{"status":"ok","timestamp":1643822862633,"user_tz":300,"elapsed":1,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}}},"execution_count":244,"outputs":[]},{"cell_type":"code","source":["df.columns=cols\n","df[\"Target\"]=Y"],"metadata":{"id":"U9K9i1nWJrb4","executionInfo":{"status":"ok","timestamp":1643822864649,"user_tz":300,"elapsed":287,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}}},"execution_count":245,"outputs":[]},{"cell_type":"code","source":["df"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":423},"id":"7NF97FGoLsyg","executionInfo":{"status":"ok","timestamp":1643822864649,"user_tz":300,"elapsed":3,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}},"outputId":"feddc702-9d01-4f3a-e9da-51c7d00f7140"},"execution_count":246,"outputs":[{"output_type":"execute_result","data":{"text/html":["\n","
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SepalLength_cmSepalWidth_cmPetalLength_cmPetalWidth_cmTarget
05.13.51.40.20
14.93.01.40.20
24.73.21.30.20
34.63.11.50.20
45.03.61.40.20
..................
1456.73.05.22.32
1466.32.55.01.92
1476.53.05.22.02
1486.23.45.42.32
1495.93.05.11.82
\n","

150 rows × 5 columns

\n","
\n"," \n"," \n"," \n","\n"," \n","
\n","
\n"," "],"text/plain":[" SepalLength_cm SepalWidth_cm PetalLength_cm PetalWidth_cm Target\n","0 5.1 3.5 1.4 0.2 0\n","1 4.9 3.0 1.4 0.2 0\n","2 4.7 3.2 1.3 0.2 0\n","3 4.6 3.1 1.5 0.2 0\n","4 5.0 3.6 1.4 0.2 0\n",".. ... ... ... ... ...\n","145 6.7 3.0 5.2 2.3 2\n","146 6.3 2.5 5.0 1.9 2\n","147 6.5 3.0 5.2 2.0 2\n","148 6.2 3.4 5.4 2.3 2\n","149 5.9 3.0 5.1 1.8 2\n","\n","[150 rows x 5 columns]"]},"metadata":{},"execution_count":246}]},{"cell_type":"code","source":["split = StratifiedShuffleSplit(n_splits = 1, test_size=0.2, random_state=42)\n","\n","for train_index, test_index in split.split(df, df[\"Target\"]):\n"," strat_train_set = df.loc[train_index]\n"," strat_test_set = df.loc[test_index]"],"metadata":{"id":"swVNlXAmJB6A","executionInfo":{"status":"ok","timestamp":1643822867095,"user_tz":300,"elapsed":810,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}}},"execution_count":247,"outputs":[]},{"cell_type":"code","source":["df_train = strat_test_set\n","df_test = strat_train_set\n"],"metadata":{"id":"VuJuJx8sMMAv","executionInfo":{"status":"ok","timestamp":1643822868964,"user_tz":300,"elapsed":3,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}}},"execution_count":248,"outputs":[]},{"cell_type":"markdown","source":["#Clasificación tipo 1: setosa"],"metadata":{"id":"nB-mPRJGNhEo"}},{"cell_type":"code","source":["#Seleccion de valores de y\n","# Tomemos solo una caractgeristicas por motivos didacticos\n","y_train = (df_train['Target'] == 0).astype(np.float) # forma rapida, se puede one hot enconder\n","X_train = df_train.iloc[:,0:1].values\n","\n","y_test = (df_test['Target'] == 0).astype(np.float) \n","X_test = df_test.iloc[:,0:1].values"],"metadata":{"id":"WKXRADL8PUnV","executionInfo":{"status":"ok","timestamp":1643823668033,"user_tz":300,"elapsed":304,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}}},"execution_count":286,"outputs":[]},{"cell_type":"code","source":["log_reg = LogisticRegression()\n","log_reg.fit(X_train, y_train)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"KbyULs9UMLYg","executionInfo":{"status":"ok","timestamp":1643823669623,"user_tz":300,"elapsed":7,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}},"outputId":"74fd0b2f-d94a-41ef-b2cb-bd386bbf4ca6"},"execution_count":287,"outputs":[{"output_type":"execute_result","data":{"text/plain":["LogisticRegression()"]},"metadata":{},"execution_count":287}]},{"cell_type":"code","source":["print(log_reg.score(X_train,y_train))\n","print(log_reg.score(X_test,y_test))"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"KDFbZrxbRErp","executionInfo":{"status":"ok","timestamp":1643823670027,"user_tz":300,"elapsed":2,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}},"outputId":"2faf63a6-2d02-45cb-a6ad-092c67aa9555"},"execution_count":288,"outputs":[{"output_type":"stream","name":"stdout","text":["0.8\n","0.9166666666666666\n"]}]},{"cell_type":"code","source":["# Determinacion de la frontera\n","X_new = np.linspace(-10, 10, 1000).reshape(-1, 1)#Generamos los valores de X_new\n","prob = log_reg.predict_proba(X_new)"],"metadata":{"id":"lcmTh9vyeVzg","executionInfo":{"status":"ok","timestamp":1643823954531,"user_tz":300,"elapsed":355,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}}},"execution_count":289,"outputs":[]},{"cell_type":"code","source":["prob"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"fbk6_5H8egd4","executionInfo":{"status":"ok","timestamp":1643823955565,"user_tz":300,"elapsed":2,"user":{"displayName":"HERNAN DAVID SALINAS 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1.00000000e+00],\n"," [1.70552461e-12, 1.00000000e+00],\n"," [1.76703097e-12, 1.00000000e+00],\n"," ...,\n"," [9.99731163e-01, 2.68837303e-04],\n"," [9.99740526e-01, 2.59473754e-04],\n"," [9.99749564e-01, 2.50436255e-04]])"]},"metadata":{},"execution_count":290}]},{"cell_type":"code","source":["decision_boundary = X_new[prob[:, 0] >= 0.5][0]\n","decision_boundary"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"0oX5-V8Bc8Z2","executionInfo":{"status":"ok","timestamp":1643823971326,"user_tz":300,"elapsed":292,"user":{"displayName":"HERNAN DAVID SALINAS 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Logistica\n","plt.plot(X_new, prob[:, 0], \"g-\", linewidth=2, label=\"Setosa\") \n","# Forntera de desicion\n","plt.plot(X_train[y_train==0], y_train[y_train==0],\"mo\",label = \"Setosa\")\n","plt.plot(X_train[y_train==1], y_train[y_train==1],\"rv\",alpha=0.2,label=\"No Setosa\")\n","plt.xlim(0.0,10)\n","plt.legend()\n","plt.vlines(decision_boundary, 0,1)\n","plt.show()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":265},"id":"SK7yN_6bMLdY","executionInfo":{"status":"ok","timestamp":1643824052228,"user_tz":300,"elapsed":758,"user":{"displayName":"HERNAN DAVID SALINAS 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\n","text/plain":["
"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":["# Tarea 8.1\n","\n","¿Entrenar con más caracteristicas y con base a las probabilidades y dado un input definir a que clase pertenece: 'versicolor', 'virginica' ?\n","\n","Por ejemplo dado X = [4.9,5.0, 1.8, 0.3] asociados a todas las caracteristicas, ¿cuál es la probabilidad de que la flor sea setosa, versicolor o virginica?\n","\n","\n"],"metadata":{"id":"1IVtgPpS0qL2"}},{"cell_type":"markdown","source":["# SOFTMAX REGRESION \n","\n","La elección anterior es conocida com softmax regresión, que permite definir un conjunto de probabilidades asociadas a un conjunto de clases. Al definir el maximo valor de la probabilidad dado un conjunto de inputs se tiene el objeto que predice el modelo, una forma de hacer una implementación rapida es mostrada a continuación."],"metadata":{"id":"A4mYFAor0x7i"}},{"cell_type":"code","source":["# Para todas las clases se puede realizar facilmente a traves de \n","# lo siguiente\n","\n","y_train = df_train['Target'] \n","X_train = df_train.iloc[:,0:1].values\n","\n","y_test = df_test['Target'] \n","X_test = df_test.iloc[:,0:1].values"],"metadata":{"id":"48oUQByoxkmw","executionInfo":{"status":"ok","timestamp":1643827977037,"user_tz":300,"elapsed":301,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}}},"execution_count":304,"outputs":[]},{"cell_type":"code","source":["softmax_reg = LogisticRegression(multi_class=\"multinomial\",solver=\"lbfgs\", \\\n"," C=10, random_state=42)\n","softmax_reg.fit(X_train, y_train)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"vLF_YXh4yH4f","executionInfo":{"status":"ok","timestamp":1643828152247,"user_tz":300,"elapsed":279,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}},"outputId":"d62882d6-da93-4049-9f58-7d63d678f269"},"execution_count":314,"outputs":[{"output_type":"execute_result","data":{"text/plain":["LogisticRegression(C=10, multi_class='multinomial', random_state=42)"]},"metadata":{},"execution_count":314}]},{"cell_type":"code","source":["X_new = np.linspace(0, 10, 1).reshape(-1,1)\n","softmax_reg.predict_proba(X)\n","#Probabilidad de pertencer a la clase cero"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"5zjeb9pByc6e","executionInfo":{"status":"ok","timestamp":1643828203908,"user_tz":300,"elapsed":296,"user":{"displayName":"HERNAN DAVID SALINAS JIMENEZ","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GhhqE42gxIAwMUb_XNY4cOCO_qFhATXyC1aSQ-Uv75lgpIzjASeZdksUxCtKp6HOhw1P_mNMjavqxjO4aOzFcrEY-ThYP9D7Ekee027FhaUTtdaaFhoWS5_FFU8kxWTMvr_JZdVNrJyfeEMLRqtBEKeyKjy7pRHipo06ksRxddL_Ql0iPCj111PoyCsKLmFgFqZMv0msm32eJF_oS-tmQMbaj8PH_EOdw4oQ7dkLvSTuJFaKaVOUx1v4Wu5CMGI-A_rn3mSBLfj7komfVsYE2AURJq8lh8dmplPvygGi35VWpCB9I01rcbaWGE3A3CuVifi4FSATNZ8V23hXImOKTHfRNHorpMOSwOQ_KeoxR9NNcM4IzArPL1NBYknrm-2CGweXdeHRO8CsJeixCd0BkOCnYvaO57ppC1rqQaXlQ66wjtagQe5nXOGb65jxHcguSCJrMLTPiYD-mWCwChCMA5_z5V4dF7a2_dOAfZWrMtjiB55m0t0jM2-1JLa2WHb8YQ8IqiPjrb8j9k5U7Gcj6eLGTCNmKFwj07d7d9PRgBVCojkgw5ZU--09pm65188t02acPA_z4nqOMpgOjib2TgskROxYAg4dT8bbvfswl5UL03KjKIHpwecuvtCZu41qMzwYcqhTFnZi8k4BTeMh4GZZrhNlVn-B1bYRwkYm5mxjZlwa1XL_6-S8vzvfkeR4OVhSYCcdBjkygl_secRGmIBp96OWWwUM5jxX_2QGHW58CWG-Aka5hfE_uQGWmNVrC-qGLc=s64","userId":"00408651407692255291"}},"outputId":"53322f88-f4af-4d5b-a1c3-0f3044682f4d"},"execution_count":319,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[9.99996616e-01, 3.38436332e-06, 1.52026712e-11]])"]},"metadata":{},"execution_count":319}]},{"cell_type":"markdown","source":["# Tarea 8.2\n","\n","1. Entrenar el modelo anterior para un numero mayor de caracteristicas\n","2. Analizar que pasa con la regularaización.\n","3. Hacer una analisis de las metricas, construir curvas de aprendizaje para todo el conjunto de datos\n","4. Con base en el libro [Hand on Machine learning](https://github.com/ageron/handson-ml/blob/master/04_training_linear_models.ipynb), constrnuir las fronteras de desición para este multiclasificador."],"metadata":{"id":"_YjRTvf5zQkZ"}},{"cell_type":"markdown","source":["\n","Referencias\n","\n","[1] http://cs229.stanford.edu/syllabus.html\n","\n","[2] https://www.coursera.org/learn/machine-learning. Week 3.\n","\n","[3] https://scikit-learn.org/stable/auto_examples/classification/plot_classifier_comparison.html#sphx-glr-auto-examples-classification-plot-classifier-comparison-py\n","\n","\n","[4]https://scikit-learn.org/stable/datasets/toy_dataset.html"],"metadata":{"id":"0h5hfX6pD0m-"}}]}