4. Regularization_and_Gradient_Descent_Exercises.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regularização e Gradiente Descendente\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introdução\n",
    "\n",
    "Vamos iniciar essa lista com um pequeno tutorial sobre regressão, atributos polinomiais e regularização em uma base de dados bem simples contendo uma coluna de variáveis `x` e um valor `y` associado. A base de dados é chamada de `X_Y_Sinusoid_Data.csv`. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "run_control": {
     "marked": true
    }
   },
   "source": [
    "## Exercício 1\n",
    "\n",
    "* Importe a base de dados. \n",
    "* Gere aproximadamente  100 pontos x na faixa de 0 a 1 utilizando a função `linspace` do `numpy`. Usando esses pontos, calcule o ponto y representando o valor verdadeiro a partir da equação: $y = sin(2\\pi x)$\n",
    "\n",
    "* Plote a base e `x` vs `y` da base e o gerado.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "filepath = 'data/X_Y_Sinusoid_Data.csv'\n",
    "data = pd.read_csv(filepath)\n",
    "\n",
    "X_real = np.linspace(0.0, 1.0, num=100)\n",
    "Y_real = np.sin(2*np.pi*X_real)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-03-10T19:32:58.021116Z",
     "start_time": "2017-03-10T14:32:58.015025-05:00"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "% matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-03-10T19:32:58.921638Z",
     "start_time": "2017-03-10T14:32:58.668630-05:00"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20ad1ea2be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.set_style('white')\n",
    "sns.set_context('talk')\n",
    "sns.set_palette('dark')\n",
    "\n",
    "# Plot of the noisy (sparse)\n",
    "ax = data.set_index('x')['y'].plot(ls='', marker='o', label='base de dados')\n",
    "ax.plot(X_real, Y_real, ls='--', marker='', label='função real')\n",
    "\n",
    "ax.legend()\n",
    "ax.set(xlabel='x data', ylabel='y data');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercício 2\n",
    "\n",
    "\n",
    "* Usando a classe `PolynomialFeatures` da biblioteca de pré-processamento do Scikit-learn's, crie atributos polinomiais de ordem 20.\n",
    "* Crie um modelo de regressão linear. \n",
    "* Plote o valor predito com o valor calculado.\n",
    "\n",
    "Note que `PolynomialFeatures` requer um dataframe com 1 coluna ou uma array bidimensional de dimensão (`n`, 1), com `n` sendo o número de amostras."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-03-10T19:57:23.344020Z",
     "start_time": "2017-03-10T14:57:23.057905-05:00"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20ad1eeb278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "# Setup the polynomial features\n",
    "degree = 20\n",
    "pf = PolynomialFeatures(degree)\n",
    "lr = LinearRegression()\n",
    "\n",
    "# Extraindo x e y da base de dados no formato correto\n",
    "X_data = data[['x']]\n",
    "Y_data = data['y']\n",
    "\n",
    "# Create the features and fit the model\n",
    "X_poly = pf.fit_transform(X_data)\n",
    "lr.fit(X_poly, Y_data)\n",
    "Y_pred = lr.predict(X_poly)\n",
    "\n",
    "# Plot the result\n",
    "plt.plot(X_data, Y_data, marker='o', ls='', label='base de dados', alpha=1)\n",
    "plt.plot(X_real, Y_real, ls='--', label='função real')\n",
    "plt.plot(X_data, Y_pred, marker='^', alpha=.5, label='predições com atributos polinomiais')\n",
    "plt.legend()\n",
    "ax = plt.gca()\n",
    "ax.set(xlabel='x data', ylabel='y data');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercício 3\n",
    "\n",
    "* Repita o experimento anterior utilizando ridge regression ($\\alpha$=0.001) e lasso regression ($\\alpha$=0.0001). \n",
    "* Plote os resultados.\n",
    "* Em seguida vamos plotar a magnitude dos coefientes dos modelos para comparação.\n",
    "\n",
    "O que a diferença entre as magnitudes te diz sobre a regularização?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-03-10T20:11:47.526408Z",
     "start_time": "2017-03-10T15:11:47.216623-05:00"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20ad0bb2438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Mute the sklearn warning about regularization\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore', module='sklearn')\n",
    "\n",
    "from sklearn.linear_model import Ridge, Lasso\n",
    "\n",
    "# Crie o modelo Ridge\n",
    "rr = Ridge(alpha = 0.001)\n",
    "rr.fit(X_poly, Y_data)\n",
    "Y_pred_rr = rr.predict(X_poly)\n",
    "\n",
    "# Crie o modelo Lasso\n",
    "lassor = Lasso(alpha = 0.0001)\n",
    "lassor.fit(X_poly, Y_data)\n",
    "Y_pred_lr = lassor.predict(X_poly)\n",
    "\n",
    "# Vamos plotar as predições\n",
    "plt.plot(X_data, Y_data, marker='o', ls='', label='base de dados')\n",
    "plt.plot(X_real, Y_real, ls='--', label='função real')\n",
    "plt.plot(X_data, Y_pred, label='regressão linear', marker='^', alpha=.5)\n",
    "plt.plot(X_data, Y_pred_rr, label='regressão ridge', marker='^', alpha=.5)\n",
    "plt.plot(X_data, Y_pred_lr, label='regressão lasso', marker='^', alpha=.5)\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.set(xlabel='x data', ylabel='y data');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>linear regression</th>\n",
       "      <th>ridge regression</th>\n",
       "      <th>lasso regression</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>2.100000e+01</td>\n",
       "      <td>21.000000</td>\n",
       "      <td>21.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>5.777551e+13</td>\n",
       "      <td>2.169397</td>\n",
       "      <td>2.167284</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>6.031941e+13</td>\n",
       "      <td>2.900278</td>\n",
       "      <td>4.706731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.619371e+07</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>3.416390e+12</td>\n",
       "      <td>0.467578</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>3.621188e+13</td>\n",
       "      <td>1.017272</td>\n",
       "      <td>0.252181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1.070540e+14</td>\n",
       "      <td>2.883507</td>\n",
       "      <td>1.641353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.655347e+14</td>\n",
       "      <td>12.429635</td>\n",
       "      <td>20.176708</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       linear regression  ridge regression  lasso regression\n",
       "count       2.100000e+01         21.000000         21.000000\n",
       "mean        5.777551e+13          2.169397          2.167284\n",
       "std         6.031941e+13          2.900278          4.706731\n",
       "min         1.619371e+07          0.000000          0.000000\n",
       "25%         3.416390e+12          0.467578          0.000000\n",
       "50%         3.621188e+13          1.017272          0.252181\n",
       "75%         1.070540e+14          2.883507          1.641353\n",
       "max         1.655347e+14         12.429635         20.176708"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Vamos examinar os coeficientes gerados pelos modelos\n",
    "# .ravel() retorna uma array multidimensional concatenada em uma dimensão (flattened)\n",
    "\n",
    "coefficients = pd.DataFrame()\n",
    "coefficients['linear regression'] = lr.coef_.ravel()\n",
    "coefficients['ridge regression'] = rr.coef_.ravel()\n",
    "coefficients['lasso regression'] = lassor.coef_.ravel()\n",
    "coefficients = coefficients.applymap(abs)\n",
    "\n",
    "coefficients.describe()  # Diferença enorme da escala da regressão linear e das regularizações"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-03-10T20:39:37.722464Z",
     "start_time": "2017-03-10T15:39:37.347911-05:00"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20ad1fd2748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "colors = sns.color_palette()\n",
    "\n",
    "# Vamos criar dois eixos, um para regressão linear outro para as regularizações\n",
    "ax1 = plt.axes()\n",
    "ax2 = ax1.twinx()\n",
    "\n",
    "# Plotar a regressão linear\n",
    "ax1.plot(lr.coef_.ravel(), \n",
    "         color=colors[0], marker='o', label='linear regression')\n",
    "\n",
    "# Plotar as regularizações no outro eixo\n",
    "ax2.plot(rr.coef_.ravel(), \n",
    "         color=colors[1], marker='o', label='ridge regression')\n",
    "\n",
    "ax2.plot(lassor.coef_.ravel(), \n",
    "         color=colors[2], marker='o', label='lasso regression')\n",
    "\n",
    "# Alterar as escalas\n",
    "ax1.set_ylim(-2e14, 2e14)\n",
    "ax2.set_ylim(-25, 25)\n",
    "\n",
    "# Combinar as legendas\n",
    "h1, l1 = ax1.get_legend_handles_labels()\n",
    "h2, l2 = ax2.get_legend_handles_labels()\n",
    "ax1.legend(h1+h2, l1+l2)\n",
    "\n",
    "ax1.set(xlabel='coefficients',ylabel='linear regression')\n",
    "ax2.set(ylabel='ridge and lasso regression')\n",
    "\n",
    "ax1.set_xticks(range(len(lr.coef_)));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercício 4\n",
    "\n",
    "Para os próximos exercícios vamos utilizar a base de dados da atividade anterior sobre o preço dos imóveis.\n",
    "\n",
    "Para começar:\n",
    "\n",
    "* Importe os dados com Pandas e aplique o one-hot-encoding nas variáveis categóricas, vamos utilizar o método `.get_dummies`. \n",
    "* Divida a base entre treino e teste. \n",
    "* Aplique a função de transformação Log nos atributos com viés. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-03-10T17:01:04.174800Z",
     "start_time": "2017-03-10T12:01:04.142735-05:00"
    }
   },
   "outputs": [],
   "source": [
    "filepath = 'data/Ames_Housing_Sales.csv'\n",
    "data1 = pd.read_csv(filepath, sep=',')\n",
    "data = data1.dropna()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-03-10T02:40:49.956043Z",
     "start_time": "2017-03-09T21:40:49.950878-05:00"
    }
   },
   "source": [
    "Crie uma lista de atributos categóricos e aplique o método `get_dummies` para gerar os atributos one-hot-encoding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-03-10T17:01:05.304547Z",
     "start_time": "2017-03-10T12:01:05.231567-05:00"
    }
   },
   "outputs": [],
   "source": [
    "# Get a Pd.Series consisting of all the string categoricals\n",
    "one_hot_encode_cols = data.dtypes[data.dtypes == np.object]  # filtering by string categoricals\n",
    "one_hot_encode_cols = one_hot_encode_cols.index.tolist()  # list of categorical fields\n",
    "\n",
    "# Primeiro devemos marcar cada coluna como categórico com pd.Categorical()\n",
    "for col in one_hot_encode_cols:\n",
    "    data[col] = pd.Categorical(data[col])\n",
    "\n",
    "# Agora aplicamos o método get_dummies() nas nossas colunas categóricas\n",
    "data = pd.get_dummies(data, columns=one_hot_encode_cols)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora, vamos dividir a base entre treino e teste, use `test_size=0.3` e `random_state=42`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-03-10T17:01:06.260979Z",
     "start_time": "2017-03-10T12:01:06.244259-05:00"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "train, test = train_test_split(data, test_size=0.3, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alguns atributos possuem valores enviesados--uma transformação log pode ajudar a aliviar essa situação. Vamos alterar esses atributos, exceto pelo `SalePrice` que é nossa variável alvo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a list of float colums to check for skewing\n",
    "mask = data.dtypes == np.float\n",
    "float_cols = data.columns[mask]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-03-10T17:01:10.689590Z",
     "start_time": "2017-03-10T12:01:10.609841-05:00"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Skew</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>MiscVal</th>\n",
       "      <td>26.915364</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PoolArea</th>\n",
       "      <td>15.777668</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LotArea</th>\n",
       "      <td>11.501694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LowQualFinSF</th>\n",
       "      <td>11.210638</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3SsnPorch</th>\n",
       "      <td>10.150612</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ScreenPorch</th>\n",
       "      <td>4.599803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFinSF2</th>\n",
       "      <td>4.466378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>EnclosedPorch</th>\n",
       "      <td>3.218303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LotFrontage</th>\n",
       "      <td>3.138032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MasVnrArea</th>\n",
       "      <td>2.492814</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>OpenPorchSF</th>\n",
       "      <td>2.295489</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SalePrice</th>\n",
       "      <td>2.106910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtFinSF1</th>\n",
       "      <td>2.010766</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TotalBsmtSF</th>\n",
       "      <td>1.979164</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1stFlrSF</th>\n",
       "      <td>1.539692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GrLivArea</th>\n",
       "      <td>1.455564</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>WoodDeckSF</th>\n",
       "      <td>1.334388</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BsmtUnfSF</th>\n",
       "      <td>0.900308</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GarageArea</th>\n",
       "      <td>0.838422</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2ndFlrSF</th>\n",
       "      <td>0.773655</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    Skew\n",
       "MiscVal        26.915364\n",
       "PoolArea       15.777668\n",
       "LotArea        11.501694\n",
       "LowQualFinSF   11.210638\n",
       "3SsnPorch      10.150612\n",
       "ScreenPorch     4.599803\n",
       "BsmtFinSF2      4.466378\n",
       "EnclosedPorch   3.218303\n",
       "LotFrontage     3.138032\n",
       "MasVnrArea      2.492814\n",
       "OpenPorchSF     2.295489\n",
       "SalePrice       2.106910\n",
       "BsmtFinSF1      2.010766\n",
       "TotalBsmtSF     1.979164\n",
       "1stFlrSF        1.539692\n",
       "GrLivArea       1.455564\n",
       "WoodDeckSF      1.334388\n",
       "BsmtUnfSF       0.900308\n",
       "GarageArea      0.838422\n",
       "2ndFlrSF        0.773655"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "skew_limit = 0.75\n",
    "skew_vals = train[float_cols].skew()\n",
    "\n",
    "skew_cols = (skew_vals\n",
    "             .sort_values(ascending=False)\n",
    "             .to_frame()\n",
    "             .rename(columns={0:'Skew'})\n",
    "             .query('abs(Skew) > {0}'.format(skew_limit)))\n",
    "\n",
    "skew_cols"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Transform all the columns where the skew is greater than 0.75, excluding \"SalePrice\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20ad19cabe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# OPTIONAL: Let's look at what happens to one of these features, when we apply np.log1p visually.\n",
    "\n",
    "field = \"BsmtFinSF1\"\n",
    "fig, (ax_before, ax_after) = plt.subplots(1, 2, figsize=(10, 5))\n",
    "train[field].hist(ax=ax_before)\n",
    "train[field].apply(np.log1p).hist(ax=ax_after)\n",
    "ax_before.set(title='before np.log1p', ylabel='frequency', xlabel='value')\n",
    "ax_after.set(title='after np.log1p', ylabel='frequency', xlabel='value')\n",
    "fig.suptitle('Field \"{}\"'.format(field));\n",
    "# a little bit better"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-03-10T17:01:15.654621Z",
     "start_time": "2017-03-10T12:01:13.780771-05:00"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
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       "      <th>2ndFlrSF</th>\n",
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       "      <th>BsmtFinSF1</th>\n",
       "      <th>BsmtFinSF2</th>\n",
       "      <th>BsmtFullBath</th>\n",
       "      <th>BsmtHalfBath</th>\n",
       "      <th>BsmtUnfSF</th>\n",
       "      <th>EnclosedPorch</th>\n",
       "      <th>...</th>\n",
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       "      <th>SaleType_Oth</th>\n",
       "      <th>SaleType_WD</th>\n",
       "      <th>Street_Grvl</th>\n",
       "      <th>Street_Pave</th>\n",
       "      <th>Utilities_AllPub</th>\n",
       "      <th>Utilities_NoSeWa</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <td>7.214504</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>5.411646</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 295 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      1stFlrSF  2ndFlrSF  3SsnPorch  BedroomAbvGr  BsmtFinSF1  BsmtFinSF2  \\\n",
       "461   6.447306  0.000000        0.0             1    6.246107         0.0   \n",
       "976   6.740519  0.000000        0.0             3    0.000000         0.0   \n",
       "1128  6.591674  6.591674        0.0             3    0.000000         0.0   \n",
       "904   6.331502  6.505784        0.0             2    5.655992         0.0   \n",
       "506   7.379008  0.000000        0.0             3    7.214504         0.0   \n",
       "\n",
       "      BsmtFullBath  BsmtHalfBath  BsmtUnfSF  EnclosedPorch        ...         \\\n",
       "461              1             0   4.753590            0.0        ...          \n",
       "976              0             0   0.000000            0.0        ...          \n",
       "1128             0             0   6.591674            0.0        ...          \n",
       "904              0             0   5.624018            0.0        ...          \n",
       "506              1             0   5.411646            0.0        ...          \n",
       "\n",
       "      SaleType_ConLD  SaleType_ConLI  SaleType_ConLw  SaleType_New  \\\n",
       "461                0               0               0             0   \n",
       "976                0               0               0             0   \n",
       "1128               0               0               0             0   \n",
       "904                0               0               0             0   \n",
       "506                0               0               0             0   \n",
       "\n",
       "      SaleType_Oth  SaleType_WD  Street_Grvl  Street_Pave  Utilities_AllPub  \\\n",
       "461              0            1            0            1                 1   \n",
       "976              0            1            0            1                 1   \n",
       "1128             0            1            0            1                 1   \n",
       "904              0            1            0            1                 1   \n",
       "506              0            1            0            1                 1   \n",
       "\n",
       "      Utilities_NoSeWa  \n",
       "461                  0  \n",
       "976                  0  \n",
       "1128                 0  \n",
       "904                  0  \n",
       "506                  0  \n",
       "\n",
       "[5 rows x 295 columns]"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Mute the setting wtih a copy warnings\n",
    "pd.options.mode.chained_assignment = None\n",
    "\n",
    "for col in skew_cols.index.tolist():\n",
    "    if col == \"SalePrice\":\n",
    "        continue\n",
    "    # aplique a função np.log1p nessa variável\n",
    "    train[col] = np.log1p(train[col])\n",
    "    test[col]  = np.log1p(test[col])\n",
    "    \n",
    "train.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos separar os atributos do preditor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-03-10T17:01:21.972625Z",
     "start_time": "2017-03-10T12:01:21.957050-05:00"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "461      86000.0\n",
       "976      84000.0\n",
       "1128    176000.0\n",
       "904     124000.0\n",
       "506     272000.0\n",
       "Name: SalePrice, dtype: float64"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_cols = [x for x in train.columns if x != 'SalePrice']\n",
    "X_train = train[feature_cols]\n",
    "y_train = train['SalePrice']\n",
    "\n",
    "X_test  = test[feature_cols]\n",
    "y_test  = test['SalePrice']\n",
    "\n",
    "y_train.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-02-21T09:11:03.256453",
     "start_time": "2017-02-21T09:11:03.241117"
    }
   },
   "source": [
    "## Exercício 5\n",
    "\n",
    "* Escreva a função **`rmse`**  que recebe valores reais da variável alvo e os peditos pelo modelo e retorna a raiz quadrada do erro quadrático médio. Use a função `mean_squared_error` do sklearn.  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "def rmse(ytrue, ypredicted):\n",
    "    return mean_squared_error(ytrue, ypredicted)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Aplique um modelo básico de regressão linear\n",
    "* imprima o rmse do modelo\n",
    "* plot os valores preditos vs reais baseado no modelo.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "93862382920.82834\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "lr = LinearRegression().fit(X_train, y_train)\n",
    "y_predicted = lr.predict(X_test)\n",
    "\n",
    "linearRegression_rmse = rmse(y_test, y_predicted)\n",
    "\n",
    "print(linearRegression_rmse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20ad2086cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = plt.figure(figsize=(6,6))\n",
    "ax = plt.axes()\n",
    "\n",
    "ax.plot(y_test, y_predicted, \n",
    "         marker='o', ls='', ms=3.0)\n",
    "\n",
    "lim = (0, y_test.max())\n",
    "\n",
    "ax.set(xlabel='Actual Price', \n",
    "       ylabel='Predicted Price', \n",
    "       xlim=lim,\n",
    "       ylim=lim,\n",
    "       title='Linear Regression Results');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercício 6\n",
    "\n",
    "A regressão Ridge usa a regularização do tipo L2 para reduzir a magnitude dos coeficientes. Isso é especialmente útil quando temos uma variância muito alta. O Scikit-Learn possui esse modelo na classe `Ridge` e uma versão que aplica validação cruzada para determinar o melhor valor de $\\alpha$ na classe `RidgeCV`.\n",
    "\n",
    "* Utilize a classe `Ridge` e determine o melhor valor de $\\alpha$ dentre os valores $$[0.005, 0.05, 0.1, 0.3, 1, 3, 5, 10, 15, 30, 80]$$ e plote o RMSE vs $\\alpha$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x20ad12a8b70>]"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20ad11dcc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "\n",
    "alphas = [0.005, 0.05, 0.1, 0.3, 1, 3, 5, 10, 15, 30, 80]\n",
    "\n",
    "rmses = []\n",
    "\n",
    "for x in alphas:\n",
    "    ridge = Ridge(alpha=x)\n",
    "    ridge.fit(X_train, y_train)\n",
    "    rmses.append(rmse(y_test, ridge.predict(X_test)))\n",
    "\n",
    "plt.title('k x acurácia')    \n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('rmse')\n",
    "\n",
    "plt.plot(rmses, alphas)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora repita o experimento utilizando RidgeCV, note que esse modelo retorna apenas o melhor $\\alpha$:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-02-21T09:48:27.914740",
     "start_time": "2017-02-21T09:48:27.293957"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15 1034855897.7516046\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import RidgeCV\n",
    "\n",
    "ridgeCV = RidgeCV(alphas=alphas, cv=4).fit(X_train, y_train)\n",
    "\n",
    "ridgeCV_rmse = rmse(y_test, ridgeCV.predict(X_test))\n",
    "\n",
    "print(ridgeCV.alpha_, ridgeCV_rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercício 7\n",
    "\n",
    "Agora utilizaremos o `LassoCV` para aplicar a regularização L1 que tenta reduzir o máximo de coeficientes para zero, fazendo uma espécie de seleção de atributos.\n",
    "\n",
    "Além disso, temos a classe `ElasticNetCV` que combina as regularizações L1 e L2.\n",
    "\n",
    "* Use o `LassoCV` e determine o $\\alpha$ ótimo e o RMSE do modelo gerado. \n",
    "* Repita com o modelo Elastic Net\n",
    "* Compare os resultados com tabelas ou plotagens\n",
    "\n",
    "Use os $\\alpha$:  \n",
    "`[1e-5, 5e-5, 0.0001, 0.0005]`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-02-21T09:50:10.797247",
     "start_time": "2017-02-21T09:50:09.006978"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0005 1541142982.9997962\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LassoCV\n",
    "\n",
    "alphas2 = np.array([1e-5, 5e-5, 0.0001, 0.0005])\n",
    "\n",
    "lassoCV = LassoCV(alphas=alphas2,\n",
    "                  max_iter=5e4,\n",
    "                  cv=3).fit(X_train, y_train)\n",
    "\n",
    "lassoCV_rmse = rmse(y_test, lassoCV.predict(X_test))\n",
    "\n",
    "print(lassoCV.alpha_, lassoCV_rmse) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos verificar quantos coeficientes são iguais a zero:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-02-21T09:50:13.053851",
     "start_time": "2017-02-21T09:50:13.047466"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Of 294 coefficients, 273 are non-zero with Lasso.\n"
     ]
    }
   ],
   "source": [
    "print('Of {} coefficients, {} are non-zero with Lasso.'.format(len(lassoCV.coef_), \n",
    "                                                               len(lassoCV.coef_.nonzero()[0])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-02-16T12:03:06.013488",
     "start_time": "2017-02-16T12:03:06.007159"
    },
    "collapsed": true,
    "run_control": {
     "marked": true
    }
   },
   "source": [
    "Agora teste o elastic net com os mesmos alphas de Lasso e l1_ratios entre 0.1 e 0.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-02-21T09:51:07.592747",
     "start_time": "2017-02-21T09:50:38.683133"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0005 0.1 1225086402.2487082\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import ElasticNetCV\n",
    "\n",
    "l1_ratios = np.linspace(0.1, 0.9, 9)\n",
    "\n",
    "elasticNetCV = ElasticNetCV(alphas=alphas2, \n",
    "                            l1_ratio=l1_ratios,\n",
    "                            max_iter=1e4).fit(X_train, y_train)\n",
    "elasticNetCV_rmse = rmse(y_test, elasticNetCV.predict(X_test))\n",
    "\n",
    "print(elasticNetCV.alpha_, elasticNetCV.l1_ratio_, elasticNetCV_rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos comparar os resultados com uma tabela:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-02-21T09:52:29.062678",
     "start_time": "2017-02-21T09:52:28.998572"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>RMSE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Linear</th>\n",
       "      <td>9.386238e+10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ridge</th>\n",
       "      <td>1.034856e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Lasso</th>\n",
       "      <td>1.541143e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ElasticNet</th>\n",
       "      <td>1.225086e+09</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    RMSE\n",
       "Linear      9.386238e+10\n",
       "Ridge       1.034856e+09\n",
       "Lasso       1.541143e+09\n",
       "ElasticNet  1.225086e+09"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rmse_vals = [linearRegression_rmse, ridgeCV_rmse, lassoCV_rmse, elasticNetCV_rmse]\n",
    "\n",
    "labels = ['Linear', 'Ridge', 'Lasso', 'ElasticNet']\n",
    "\n",
    "rmse_df = pd.Series(rmse_vals, index=labels).to_frame()\n",
    "rmse_df.rename(columns={0: 'RMSE'}, inplace=1)\n",
    "rmse_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternativamente podemos fazer um plot do valor real vs predito para cada modelo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-02-21T09:53:54.142116",
     "start_time": "2017-02-21T09:53:53.857081"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20ad10f21d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = plt.figure(figsize=(6,6))\n",
    "ax = plt.axes()\n",
    "\n",
    "labels = ['Ridge', 'Lasso', 'ElasticNet']\n",
    "\n",
    "models = [ridgeCV, lassoCV, elasticNetCV]\n",
    "\n",
    "for mod, lab in zip(models, labels):\n",
    "    ax.plot(y_test, mod.predict(X_test), \n",
    "             marker='o', ls='', ms=3.0, label=lab)\n",
    "\n",
    "\n",
    "leg = plt.legend(frameon=True)\n",
    "leg.get_frame().set_edgecolor('black')\n",
    "leg.get_frame().set_linewidth(1.0)\n",
    "\n",
    "ax.set(xlabel='Actual Price', \n",
    "       ylabel='Predicted Price', \n",
    "       title='Linear Regression Results');"
   ]
  }
 ],
 "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}