Regresión Lineal Regularizada.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from module import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.loadtxt('Admission_Predict.csv',delimiter=\",\", skiprows=1)[:,1:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Se normalizarán los datos para tener una escala más uniforme y un mejor modelo. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#normalización de data \n",
    "norm_t_set = np.array([np.zeros(len(data))])\n",
    "for arr in data.T:\n",
    "    norm_tuple = []\n",
    "    for index in range(len(arr)):\n",
    "        norm_tuple.append((arr[index] - arr.min())/ (arr.max()- arr.min()))\n",
    "    norm_t_set = np.vstack((norm_t_set, np.array(norm_tuple)))\n",
    "data = norm_t_set[1:,]\n",
    "data = data.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Separación de data en sets de training, cross validation y testing. La separación se realizará mediante índices aleatorios sin repetir, y la data será repartida de 60% (240 datos) para el training set, 20% (80 datos) para el cross validation set y 20% (80 datos) para el test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Seleccionar conjunto de training y test\n",
    "\n",
    "t_set = np.zeros(8).reshape((1,8))\n",
    "cv_set = np.zeros(8).reshape((1,8))\n",
    "test = np.zeros(8).reshape((1,8))\n",
    "func = [t_set, cv_set, test]\n",
    "perc = [240, 80, 80]\n",
    "t_rand = []\n",
    "for x in range(3):\n",
    "    while(len(func[x]) < perc[x]+1):\n",
    "        r = random.randint(0,399)\n",
    "        if r not in t_rand: \n",
    "            t_rand.append(r)\n",
    "            func[x] = np.concatenate((func[x], data[r].reshape((1,8))))\n",
    "            \n",
    "t_set, cv_set, test = func[0][1:,], func[1][1:,], func[2][1:,]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Establecimiento de modelo \n",
    "\n",
    "Para el modelo, se tomarán todos los features del dataset, exceptuando el Serial No. (ya que no tiene correlación alguna con la variable de Chance of Admit ni provee información útil)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = t_set[:,len(t_set[0])-1:len(t_set[0])]\n",
    "\n",
    "X = np.vstack((\n",
    "    np.ones(len(t_set)),\n",
    "    t_set[:,:7].T,\n",
    ")).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "m, n = X.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generación de de vector theta inicial; después de múltiples generaciones aleatorias del vector theta_0, el vector que daba los mejores resultados es el siguiente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_0 = np.array([[-0.06706054],\n",
    " [ 0.21327747],\n",
    " [-0.19349977],\n",
    " [ 0.10454866],\n",
    " [-0.06015129],\n",
    " [ 0.28915204],\n",
    " [ 0.27315269],\n",
    " [-0.00179598]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Cálculo de descenso al gradiente\n",
    "theta = gradient_descent(\n",
    "    X,\n",
    "    y,\n",
    "    theta_0,\n",
    "    linear_cost_regular,\n",
    "    linear_cost_derivate_regular,\n",
    "    alpha=0.001,\n",
    "    threshold=0.001,\n",
    "    max_iter= 300000,\n",
    "    lamda=0\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_predic = np.matmul(X, theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8073937589533833"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Cálculo de coeficiente de determinación (R^2) para saber qué tan bueno fue el fit del modelo. \n",
    "\n",
    "r2_t = (((y-y.mean())**2).sum()-((np.matmul(X, theta)-y)**2).sum())/((y-y.mean())**2).sum()\n",
    "r2_t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.011113734056933661"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Cálculo de Error Cuadrático Medio para saber qué tanto se equivocó el modelo \n",
    "ecm_t = (1/len(t_set))*((y_predic-y)**2).sum()\n",
    "ecm_t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En la siguiente gráfica se ejemplifica qué tan parecido fue la predicción del modelo, al valor real de Chance of Admit. Se establecerá un feature cualquiera en el eje X (se tomó la feature de GRE Score, pero realmente pudo haber sido cualquiera), porque lo que interesa es ver cómo se plotean los puntos en el eje Y."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 1], y)\n",
    "plt.scatter(X[:, 1], y_predic, color='red')\n",
    "plt.title('Scatter plot GRE Score vs. Chance of Admit')\n",
    "plt.xlabel('Chance of Admit')\n",
    "plt.ylabel('GRE Score')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cross-Validation\n",
    "Después de obtener el theta que mejor resultados brinda, se realizan las pruebas con el cross-validation set para tunear de mejor manera el modelo. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Generación de modelo para los datos del set de cross validation\n",
    "cv_x = np.vstack((\n",
    "    np.ones(len(cv_set)),\n",
    "    cv_set[:,:7].T\n",
    ")).T\n",
    "\n",
    "\n",
    "cv_y = cv_set[:,len(cv_set[0])-1:len(cv_set[0])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "#descenso al gradiente para datos del CV set. \n",
    "theta = gradient_descent(\n",
    "    cv_x,\n",
    "    cv_y,\n",
    "    theta_0,\n",
    "    linear_cost_regular,\n",
    "    linear_cost_derivate_regular,\n",
    "    alpha=0.001,\n",
    "    threshold=0.001,\n",
    "    max_iter= 300000,\n",
    "    lamda=0\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7698726856780918"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Cálculo de coeficiente de determinación (R^2)\n",
    "r2_cv = (((cv_y-cv_y.mean())**2).sum()-((np.matmul(cv_x, theta)-cv_y)**2).sum())/((cv_y-cv_y.mean())**2).sum()\n",
    "r2_cv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.009107249326991166"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Error Cuadrático Medio\n",
    "ecm = (1/len(cv_set))*((np.matmul(cv_x, theta)-cv_y)**2).sum()\n",
    "ecm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similar a lo realizado para el set de datos para training, se graficará la predicción vs el valor real estableciendo en el eje X un feature cualquiera del modelo. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(cv_x[:, 1], cv_y)\n",
    "plt.scatter(cv_x[:, 1], np.matmul(cv_x, theta), color='red')\n",
    "plt.title('Scatter plot GRE Score vs. Chance of Admit')\n",
    "plt.xlabel('Chance of Admit')\n",
    "plt.ylabel('GRE Score')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regularización del modelo \n",
    "\n",
    "Con los resultados de R^2 y el Error Cuadrático Medio obtenidos previamente se puede observar que el modelo funciona bastante bien con el set de datos de cross validation. Aún así, se presentarán las gráficas de costo vs. complejidad del modelo y costo vs. lambda para observar si es posible encontrar un mejor modelo. Se definirá como complejidad a la cantidad de features incluídas en el modelo, hasta ahora se ha trabajado con una complejidad de 7. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "#ECM para datos de training\n",
    "t_ecm = np.array([])\n",
    "t_lamdas = np.linspace(-15, 30, 15)\n",
    "\n",
    "#iteración para obtener ECM con distintos valores de lambda\n",
    "for l in t_lamdas:\n",
    "    theta = gradient_descent(\n",
    "        X,\n",
    "        y,\n",
    "        theta_0,\n",
    "        linear_cost_regular,\n",
    "        linear_cost_derivate_regular,\n",
    "        alpha=0.001,\n",
    "        threshold=0.001,\n",
    "        max_iter=30000,\n",
    "        lamda=l)\n",
    "    ecm = (1/len(t_set))*((np.matmul(X, theta)-y)**2).sum()\n",
    "    t_ecm = np.append(t_ecm, ecm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "#ECM para datos de cross validation\n",
    "cv_ecm = np.array([])\n",
    "cv_lamdas = np.linspace(-15, 30, 15)\n",
    "\n",
    "for l in cv_lamdas:\n",
    "    theta = gradient_descent(\n",
    "        cv_x,\n",
    "        cv_y,\n",
    "        theta_0,\n",
    "        linear_cost_regular,\n",
    "        linear_cost_derivate_regular,\n",
    "        alpha=0.001,\n",
    "        threshold=0.001,\n",
    "        max_iter=30000,\n",
    "        lamda=l)\n",
    "    ecm = (1/len(cv_set))*((np.matmul(cv_x, theta)-cv_y)**2).sum()\n",
    "    cv_ecm = np.append(cv_ecm, ecm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7Kx3UEXHtAn7sFUlrzli+uDW2XFXt753La7ZXR8Srtler2Kpa9myvUhHSYxHx7dZwJediSkQctb1dxQ3AL7C9srVV3fH3CLs+5u8xSTfY/hXbQ5IukbSryz2l9BNJl7SOap+n4kDqY13uqZsek3Rj6/sbJS37//Nysel8j6R9EXHHGU9VcS5qrS1p2X6vpE+r2Ge/XdIXWqt1fC74ZOIsbP+RpH+UVJN0VNKeiLiu9dxmSTepOBp+S0R8v2uNLgHbn5V0l6Zvbrylyy0tCdvflHS1istYvibpbyQ9IulBSWtVXMr3TyPi7AOOy4rtqyT9h6TnJJ1qDf+1iv3UVZuL31FxsLBPxYbugxHxd7Z/XcWB9g9KekbSlyLieMd+L0ENAHlj1wcAZI6gBoDMEdQAkDmCGgAyR1ADQOYIagDIHEENAJn7P11XWXb6zRdVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(t_lamdas, t_ecm, color='green')\n",
    "plt.scatter(cv_lamdas, cv_ecm, color='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Se volverán a realizar las gráficas anteriores para poder observar de mejor manera cuál es el lambda más óptimo: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "#ECM para datos de training\n",
    "t_ecm = np.array([])\n",
    "t_lamdas = np.linspace(0, 15, 10)\n",
    "\n",
    "for l in t_lamdas:\n",
    "    theta = gradient_descent(\n",
    "        X,\n",
    "        y,\n",
    "        theta_0,\n",
    "        linear_cost_regular,\n",
    "        linear_cost_derivate_regular,\n",
    "        alpha=0.001,\n",
    "        threshold=0.001,\n",
    "        max_iter=30000,\n",
    "        lamda=l)\n",
    "    ecm = (1/len(t_set))*((np.matmul(X, theta)-y)**2).sum()\n",
    "    t_ecm = np.append(t_ecm, ecm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "#ECM para datos de cross validation\n",
    "cv_ecm = np.array([])\n",
    "cv_lamdas = np.linspace(0, 15, 10)\n",
    "\n",
    "for l in cv_lamdas:\n",
    "    theta = gradient_descent(\n",
    "        cv_x,\n",
    "        cv_y,\n",
    "        theta_0,\n",
    "        linear_cost_regular,\n",
    "        linear_cost_derivate_regular,\n",
    "        alpha=0.001,\n",
    "        threshold=0.001,\n",
    "        max_iter=30000,\n",
    "        lamda=l)\n",
    "    ecm = (1/len(cv_set))*((np.matmul(cv_x, theta)-cv_y)**2).sum()\n",
    "    cv_ecm = np.append(cv_ecm, ecm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(t_lamdas, t_ecm, color='green')\n",
    "plt.scatter(cv_lamdas, cv_ecm, color='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Con la gráfica anterior se puede observar que el lambda más óptimo es de alrededor 8. Verificaremos si sí se logra mejorar la predicción. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [],
   "source": [
    "#modificacion de lambda para mejores resultados \n",
    "theta = gradient_descent(\n",
    "    cv_x,\n",
    "    cv_y,\n",
    "    theta_0,\n",
    "    linear_cost_regular,\n",
    "    linear_cost_derivate_regular,\n",
    "    alpha=0.001,\n",
    "    threshold=0.001,\n",
    "    max_iter=30000,\n",
    "    lamda=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7710520707936307"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2 = (((cv_y-cv_y.mean())**2).sum()-((np.matmul(cv_x, theta)-cv_y)**2).sum())/((cv_y-cv_y.mean())**2).sum()\n",
    "r2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00906057536161942"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Error Cuadrático Medio\n",
    "ecm = (1/len(cv_set))*((np.matmul(cv_x, theta)-cv_y)**2).sum()\n",
    "ecm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como se puede ver, la regularización sí logró la mejora del modelo, aunque no haya sido por mucho. El lambda escogido fue pequeño ya que, como se ve en la gráfica anterior, conforme va creciendo también crece el error del modelo, por lo que un lambda muy pequeño da mejores resultados que sin la regularización, a pesar que éste sea cercano a 0. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing\n",
    "\n",
    "A continuación, luego de haber obtenido un descenso al gradiente relativamente satisfactorio con el modelo establecido, se procederá a usar el mismo con el set de testing, y ver los resultados. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_test = np.vstack((\n",
    "    np.ones(len(test)),\n",
    "    test[:,:7].T\n",
    ")).T\n",
    "\n",
    "\n",
    "y_test = test[:,len(test[0])-1:len(test[0])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8108761286939817"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Cálculo de coeficiente de determinación (R^2)\n",
    "r2_test = (((y_test-y_test.mean())**2).sum()-((np.matmul(x_test, theta)-y_test)**2).sum())/((y_test-y_test.mean())**2).sum()\n",
    "r2_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.007925123789411176"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Error Cuadrático Medio\n",
    "ecm = (1/len(test))*((np.matmul(x_test, theta)-y_test)**2).sum()\n",
    "ecm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x_test[:, 1], y_test)\n",
    "plt.scatter(x_test[:, 1], np.matmul(x_test, theta), color='red')\n",
    "plt.title('Scatter plot GRE Score vs. Chance of Admit')\n",
    "plt.xlabel('Chance of Admit')\n",
    "plt.ylabel('GRE Score')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusión\n",
    "\n",
    "Con los resultados anteriores se observa que el modelo logró una predicción relativamente buena para los datos del set de testing. Se fundamenta el desempeño del modelo al observar el coeficiente de determinación (R^2) - el cual determina qué tan buen ajuste proveyó al modelo con la tendencia de los datos - calculado es bastante alto (0.81 para el set de test) e incluso el Error Cuadrático Medio - el cual estima la diferencia entre el estimador y lo que se estima - es bastante cercano a 0, lo que quiere decir que el promedio de error fue muy bajo. \n",
    "\n",
    "Adicionalmente, en el último scatter plot se visualiza gráficamente que las predicciones realizadas se ajustaron bastante bien a la nube de puntos de los valores reales. "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}