02.2.LinearRegression-sklearn.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "python version:  sys.version_info(major=3, minor=7, micro=2, releaselevel='final', serial=0)\n",
      "sklearn 0.23.2\n"
     ]
    }
   ],
   "source": [
    "import os, sys\n",
    "\n",
    "from LossJLearn.utils.plot import show_prediction_face_comparison, show_linear_point, show_regressor_linear\n",
    "from LossJLearn.datasets import load_linear_data\n",
    "\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import sklearn\n",
    "from sklearn.linear_model import LinearRegression, Ridge, RidgeCV, Lasso, SGDRegressor\n",
    "from sklearn.preprocessing import PolynomialFeatures, StandardScaler, Normalizer\n",
    "from sklearn.datasets import fetch_olivetti_faces, fetch_california_housing, load_diabetes\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "print(\"python version: \", sys.version_info)\n",
    "print(sklearn.__name__, sklearn.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. 基础回归"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1 线性回归"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.1.1 sklearn.linear_model.LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html#sklearn.linear_model.LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([3.22193235]), -5.178908572151361)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_data, y_data = load_linear_data(point_count=500, max_=10, w=3.2412, b=-5.2941, random_state=10834)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X_data, y_data, random_state=19332)\n",
    "\n",
    "rgs = LinearRegression(fit_intercept=True, normalize=False, copy_X=True, n_jobs=None)\n",
    "rgs.fit(X_train, y_train)\n",
    "rgs.coef_, rgs.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.987886225859275"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_regressor_linear(X_test, y_test, rgs.coef_, rgs.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 正规化Normalizer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "每个样本求范数，再用每个特征除以范数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "norm = Normalizer(norm=\"l2\", copy=True)\n",
    "X_train_norm = norm.fit_transform(X_train)\n",
    "X_test_norm = norm.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.]), 10.954228474432476)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs = LinearRegression()\n",
    "rgs.fit(X_train_norm, y_train)\n",
    "rgs.coef_, rgs.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.007907420757761408"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs.score(X_test_norm, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[1.],\n",
       "        [1.],\n",
       "        [1.],\n",
       "        [1.],\n",
       "        [1.],\n",
       "        [1.],\n",
       "        [1.],\n",
       "        [1.],\n",
       "        [1.],\n",
       "        [1.]]), array([[1.],\n",
       "        [1.],\n",
       "        [1.],\n",
       "        [1.],\n",
       "        [1.],\n",
       "        [1.],\n",
       "        [1.],\n",
       "        [1.],\n",
       "        [1.],\n",
       "        [1.]]))"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train_norm[:10], X_test_norm[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[8.51310884],\n",
       "       [2.56333264],\n",
       "       [6.69031165],\n",
       "       [6.78072578],\n",
       "       [7.17228023]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.06177273],\n",
       "       [-0.04306255],\n",
       "       [ 0.02965497],\n",
       "       [ 0.03124807],\n",
       "       [ 0.03814728]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs = LinearRegression(fit_intercept=True, \n",
    "                       normalize=True, # bool. fit_intercept为True才生效。 如果为True，则将在回归之前通过减去均值并除以12范数来对回归变量X进行归一化。\n",
    "                       copy_X=False, \n",
    "                       n_jobs=None)\n",
    "rgs.fit(X_train, y_train)\n",
    "X_train[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.72985206],\n",
       "       [7.73380008],\n",
       "       [3.07655716],\n",
       "       [0.17534075],\n",
       "       [6.34958458]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.987886225859275"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.72985206],\n",
       "       [7.73380008],\n",
       "       [3.07655716],\n",
       "       [0.17534075],\n",
       "       [6.34958458]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([3.22193235]), -5.178908572151364)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs.coef_, rgs.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "327 µs ± 20 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "rgs = LinearRegression(n_jobs=2)\n",
    "rgs.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "354 µs ± 66.7 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "rgs = LinearRegression(n_jobs=-1)\n",
    "rgs.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "376 µs ± 35.8 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "rgs = LinearRegression(n_jobs=None)\n",
    "rgs.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.1.2 sklearn.linear_model.SGDRegressor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.SGDRegressor.html#sklearn.linear_model.SGDRegressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_data, y_data = load_linear_data(point_count=500, max_=10, w=3.2412, b=-5.2941, random_state=10834)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X_data, y_data, random_state=19332)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9874157381106864"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs = SGDRegressor(random_state=10190)\n",
    "rgs.fit(X_train, y_train)\n",
    "rgs.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 标准化StandardScaler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.StandardScaler.html#sklearn.preprocessing.StandardScaler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "z = (x - u) / s, u是均值， s是标准差"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "scaler = StandardScaler(copy=True, with_mean=True, with_std=True)\n",
    "X_train_scaler = scaler.fit_transform(X_train)\n",
    "X_test_scaler = scaler.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([5.00728609]), array([2.93074174]))"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaler.mean_, scaler.scale_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([9.43581359]), array([10.94787748]))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs = SGDRegressor(\n",
    "    loss='squared_loss', # ‘squared_loss’, ‘huber’, ‘epsilon_insensitive’, or ‘squared_epsilon_insensitive’\n",
    "    penalty='l2', # 惩罚项（正则项）\n",
    "    alpha=0.0001, # 正则系数\n",
    "    fit_intercept=True, \n",
    "    max_iter=100,\n",
    "    tol=0.001,\n",
    "    shuffle=True,\n",
    "    verbose=0,\n",
    "    epsilon=0.1,\n",
    "    random_state=10190, \n",
    "    learning_rate='invscaling', \n",
    "    eta0=0.01,\n",
    "    power_t=0.25,\n",
    "    early_stopping=True,\n",
    "    validation_fraction=0.1,\n",
    "    n_iter_no_change=5,\n",
    "    warm_start=False,\n",
    "    average=False\n",
    ")\n",
    "rgs.fit(X_train_scaler, y_train)\n",
    "rgs.coef_, rgs.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9878711884871213"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs.score(X_test_scaler, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_regressor_linear(X_test_scaler, y_test, pred_coef=rgs.coef_, pred_intercept=rgs.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 多项式回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def load_data_from_func(func=lambda X_data: 0.1383 * np.square(X_data) - 1.2193 * X_data + 2.4096,\n",
    "                        x_min=0, x_max=10, n_samples=500, loc=0, scale=1, random_state=None):\n",
    "    if random_state is not None and isinstance(random_state, int):\n",
    "        np.random.seed(random_state)\n",
    "    x = np.random.uniform(x_min, x_max, n_samples)\n",
    "    y = func(x)\n",
    "    noise = np.random.normal(loc=loc, scale=scale, size=n_samples)\n",
    "    y += noise\n",
    "    return x.reshape([-1, 1]), y\n",
    "\n",
    "X_data, y_data = load_data_from_func(n_samples=500, random_state=10392)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.PolynomialFeatures.html#sklearn.preprocessing.PolynomialFeatures/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(375, 3)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X_data, y_data, random_state=10319)\n",
    "poly = PolynomialFeatures() # [1, a, b, a^2, ab, b^2]\n",
    "X_train_poly = poly.fit_transform(X_train)\n",
    "X_test_poly = poly.transform(X_test)\n",
    "\n",
    "X_train_poly.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5423800412888162"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs = LinearRegression()\n",
    "rgs.fit(X_train_poly, y_train)\n",
    "rgs.score(X_test_poly, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred = rgs.predict(X_test_poly)\n",
    "\n",
    "def show_regression_line(X_data, y_data, y_pred):\n",
    "    plt.figure(figsize=[10, 5])\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"y\")\n",
    "    if X_data.ndim == 2:\n",
    "        X_data = X_data.reshape(-1)\n",
    "    plt.scatter(X_data, y_data)\n",
    "    idx = np.argsort(X_data)\n",
    "    X_data = X_data[idx]\n",
    "    y_pred = y_pred[idx]\n",
    "    plt.plot(X_data, y_pred, color=\"darkorange\")\n",
    "    plt.show()\n",
    "    \n",
    "show_regression_line(X_test, y_test, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. 加利福尼亚房价数据集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = fetch_california_housing(data_home=\"./data\", as_frame=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_data = df['data']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "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>MedInc</th>\n",
       "      <th>HouseAge</th>\n",
       "      <th>AveRooms</th>\n",
       "      <th>AveBedrms</th>\n",
       "      <th>Population</th>\n",
       "      <th>AveOccup</th>\n",
       "      <th>Latitude</th>\n",
       "      <th>Longitude</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "      <td>20640.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.870671</td>\n",
       "      <td>28.639486</td>\n",
       "      <td>5.429000</td>\n",
       "      <td>1.096675</td>\n",
       "      <td>1425.476744</td>\n",
       "      <td>3.070655</td>\n",
       "      <td>35.631861</td>\n",
       "      <td>-119.569704</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.899822</td>\n",
       "      <td>12.585558</td>\n",
       "      <td>2.474173</td>\n",
       "      <td>0.473911</td>\n",
       "      <td>1132.462122</td>\n",
       "      <td>10.386050</td>\n",
       "      <td>2.135952</td>\n",
       "      <td>2.003532</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.499900</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.846154</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>0.692308</td>\n",
       "      <td>32.540000</td>\n",
       "      <td>-124.350000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2.563400</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>4.440716</td>\n",
       "      <td>1.006079</td>\n",
       "      <td>787.000000</td>\n",
       "      <td>2.429741</td>\n",
       "      <td>33.930000</td>\n",
       "      <td>-121.800000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>3.534800</td>\n",
       "      <td>29.000000</td>\n",
       "      <td>5.229129</td>\n",
       "      <td>1.048780</td>\n",
       "      <td>1166.000000</td>\n",
       "      <td>2.818116</td>\n",
       "      <td>34.260000</td>\n",
       "      <td>-118.490000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>4.743250</td>\n",
       "      <td>37.000000</td>\n",
       "      <td>6.052381</td>\n",
       "      <td>1.099526</td>\n",
       "      <td>1725.000000</td>\n",
       "      <td>3.282261</td>\n",
       "      <td>37.710000</td>\n",
       "      <td>-118.010000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>15.000100</td>\n",
       "      <td>52.000000</td>\n",
       "      <td>141.909091</td>\n",
       "      <td>34.066667</td>\n",
       "      <td>35682.000000</td>\n",
       "      <td>1243.333333</td>\n",
       "      <td>41.950000</td>\n",
       "      <td>-114.310000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             MedInc      HouseAge      AveRooms     AveBedrms    Population  \\\n",
       "count  20640.000000  20640.000000  20640.000000  20640.000000  20640.000000   \n",
       "mean       3.870671     28.639486      5.429000      1.096675   1425.476744   \n",
       "std        1.899822     12.585558      2.474173      0.473911   1132.462122   \n",
       "min        0.499900      1.000000      0.846154      0.333333      3.000000   \n",
       "25%        2.563400     18.000000      4.440716      1.006079    787.000000   \n",
       "50%        3.534800     29.000000      5.229129      1.048780   1166.000000   \n",
       "75%        4.743250     37.000000      6.052381      1.099526   1725.000000   \n",
       "max       15.000100     52.000000    141.909091     34.066667  35682.000000   \n",
       "\n",
       "           AveOccup      Latitude     Longitude  \n",
       "count  20640.000000  20640.000000  20640.000000  \n",
       "mean       3.070655     35.631861   -119.569704  \n",
       "std       10.386050      2.135952      2.003532  \n",
       "min        0.692308     32.540000   -124.350000  \n",
       "25%        2.429741     33.930000   -121.800000  \n",
       "50%        2.818116     34.260000   -118.490000  \n",
       "75%        3.282261     37.710000   -118.010000  \n",
       "max     1243.333333     41.950000   -114.310000  "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X_data, df.target, random_state=1, shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 线性回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs = LinearRegression()\n",
    "rgs.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5929869285760094"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.59298692857601"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaler = StandardScaler()\n",
    "X_train_scaler = scaler.fit_transform(X_train)\n",
    "X_test_scaler = scaler.transform(X_test)\n",
    "rgs = LinearRegression()\n",
    "rgs.fit(X_train_scaler, y_train)\n",
    "rgs.score(X_test_scaler, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 岭回归"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://scikit-learn.org/stable/modules/linear_model.html#ridge-regression-and-classification  \n",
    "https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.Ridge.html#sklearn.linear_model.Ridge  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5929846671576572"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs = Ridge(alpha=1.0, solver=\"auto\")\n",
    "rgs.fit(X_train, y_train)\n",
    "rgs.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.40414555e-01,  9.66110278e-03, -1.04473532e-01,  6.25231108e-01,\n",
       "       -4.61382991e-06, -3.37354852e-03, -4.24301365e-01, -4.39158870e-01])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.RidgeCV.html#sklearn.linear_model.RidgeCV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.2.1 交叉验证"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RidgeCV(alphas=array([1.e-03, 1.e-02, 1.e-01, 1.e+00, 1.e+01]), gcv_mode='auto',\n",
       "        store_cv_values=None)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs = RidgeCV(\n",
    "    alphas=(0.001, 0.01, 0.1, 1.0, 10.0),\n",
    "    fit_intercept=True,\n",
    "    normalize= False,\n",
    "    scoring=None, # 如果为None，则当cv为'auto'或为None时为负均方误差，否则为r2得分。scorer(estimator, X, y)\n",
    "    cv=None, # int, cross-validation generator or an iterable, default=None\n",
    "    gcv_mode='auto', # {‘auto’, ‘svd’, eigen’}, default=’auto’\n",
    "    store_cv_values=None, # bool, 是否将与每个alpha对应的交叉验证值存储在cv_values_属性中, 仅cv=None有效\n",
    ")\n",
    "rgs.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.5262776278210176"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs.best_score_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5929620810811334"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.605370852586254, 0.5929620792665222)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs = RidgeCV(\n",
    "    alphas=(0.001, 0.01, 0.1, 1.0, 10.0),\n",
    "    fit_intercept=True,\n",
    "    normalize= False,\n",
    "    scoring=None, # 如果为None，则当cv为'auto'或为None时为负均方误差，否则为r2得分。scorer(estimator, X, y)\n",
    "    cv=10, # int, cross-validation generator or an iterable, default=None\n",
    "    gcv_mode='auto', # {‘auto’, ‘svd’, eigen’}, default=’auto’\n",
    "    store_cv_values=None, # bool, 是否将与每个alpha对应的交叉验证值存储在cv_values_属性中, 仅cv=None有效\n",
    ")\n",
    "rgs.fit(X_train, y_train)\n",
    "rgs.best_score_, rgs.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3 索套回归"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.Lasso.html#sklearn.linear_model.Lasso   \n",
    "https://scikit-learn.org/stable/modules/linear_model.html#lasso  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.28887951253541133"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs = Lasso()\n",
    "rgs.fit(X_train, y_train)\n",
    "rgs.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.46661197e-01,  5.85834677e-03,  0.00000000e+00, -0.00000000e+00,\n",
       "       -8.83884669e-06, -0.00000000e+00, -0.00000000e+00, -0.00000000e+00])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.4 多项式回归"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.PolynomialFeatures.html?highlight=polynomialfeatures#sklearn.preprocessing.PolynomialFeatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(15480, 45)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly = PolynomialFeatures(degree=2, interaction_only=False, include_bias=True)\n",
    "X_train_poly = poly.fit_transform(X_train) # [1, a, b, a^2, ab, b^2]\n",
    "X_train_poly.shape "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['1',\n",
       " 'x0',\n",
       " 'x1',\n",
       " 'x2',\n",
       " 'x3',\n",
       " 'x4',\n",
       " 'x5',\n",
       " 'x6',\n",
       " 'x7',\n",
       " 'x0^2',\n",
       " 'x0 x1',\n",
       " 'x0 x2',\n",
       " 'x0 x3',\n",
       " 'x0 x4',\n",
       " 'x0 x5',\n",
       " 'x0 x6',\n",
       " 'x0 x7',\n",
       " 'x1^2',\n",
       " 'x1 x2',\n",
       " 'x1 x3',\n",
       " 'x1 x4',\n",
       " 'x1 x5',\n",
       " 'x1 x6',\n",
       " 'x1 x7',\n",
       " 'x2^2',\n",
       " 'x2 x3',\n",
       " 'x2 x4',\n",
       " 'x2 x5',\n",
       " 'x2 x6',\n",
       " 'x2 x7',\n",
       " 'x3^2',\n",
       " 'x3 x4',\n",
       " 'x3 x5',\n",
       " 'x3 x6',\n",
       " 'x3 x7',\n",
       " 'x4^2',\n",
       " 'x4 x5',\n",
       " 'x4 x6',\n",
       " 'x4 x7',\n",
       " 'x5^2',\n",
       " 'x5 x6',\n",
       " 'x5 x7',\n",
       " 'x6^2',\n",
       " 'x6 x7',\n",
       " 'x7^2']"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly.get_feature_names()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_test_poly = poly.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6632310603984577"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs = LinearRegression()\n",
    "rgs.fit(X_train_poly, y_train)\n",
    "rgs.score(X_test_poly, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(15480, 37)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly = PolynomialFeatures(degree=2, \n",
    "                          interaction_only=True, # 是否只保留插乘特征，除去指数项\n",
    "                          include_bias=True, \n",
    "                          order=\"C\") # Order of output array in the dense case. ‘F’ order is faster to compute, but may slow down subsequent estimators.\n",
    "X_train_poly = poly.fit_transform(X_train) \n",
    "X_test_poly = poly.transform(X_test)\n",
    "X_train_poly.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['1',\n",
       " 'x0',\n",
       " 'x1',\n",
       " 'x2',\n",
       " 'x3',\n",
       " 'x4',\n",
       " 'x5',\n",
       " 'x6',\n",
       " 'x7',\n",
       " 'x0 x1',\n",
       " 'x0 x2',\n",
       " 'x0 x3',\n",
       " 'x0 x4',\n",
       " 'x0 x5',\n",
       " 'x0 x6',\n",
       " 'x0 x7',\n",
       " 'x1 x2',\n",
       " 'x1 x3',\n",
       " 'x1 x4',\n",
       " 'x1 x5',\n",
       " 'x1 x6',\n",
       " 'x1 x7',\n",
       " 'x2 x3',\n",
       " 'x2 x4',\n",
       " 'x2 x5',\n",
       " 'x2 x6',\n",
       " 'x2 x7',\n",
       " 'x3 x4',\n",
       " 'x3 x5',\n",
       " 'x3 x6',\n",
       " 'x3 x7',\n",
       " 'x4 x5',\n",
       " 'x4 x6',\n",
       " 'x4 x7',\n",
       " 'x5 x6',\n",
       " 'x5 x7',\n",
       " 'x6 x7']"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly.get_feature_names()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6493637034603157"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rgs = LinearRegression()\n",
    "rgs.fit(X_train_poly, y_train)\n",
    "rgs.score(X_test_poly, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 总结"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. sklearn的线性回归相关的模型放在sklearn.linear_model下  \n",
    "    > from sklearn.linear_model import LinearRegression, Ridge, RidgeCV, Lasso, SGDRegressor   \n",
    "\n",
    "2. 调参数  \n",
    "    > LinearRegression(fit_intercept=True, normalize=False, copy_X=True, n_jobs=None)  \n",
    "    >  \n",
    "    > SGDRegressor(loss='squared_loss',\n",
    "    penalty='l2',\n",
    "    alpha=0.0001,\n",
    "    fit_intercept=True,\n",
    "    max_iter=1000,\n",
    "    tol=0.001,\n",
    "    shuffle=True,\n",
    "    epsilon=0.1,\n",
    "    random_state=None,\n",
    "    learning_rate='invscaling',\n",
    "    eta0=0.01,\n",
    "    early_stopping=False,\n",
    "    validation_fraction=0.1,\n",
    "    n_iter_no_change=5)   \n",
    "    >  \n",
    "    > Ridge(alpha=1.0, fit_intercept=True,\n",
    "    normalize=False,\n",
    "    copy_X=True,\n",
    "    max_iter=None,\n",
    "    tol=0.001,\n",
    "    solver='auto',\n",
    "    random_state=None)  \n",
    "    >  \n",
    "    > Lasso(alpha=1.0,\n",
    "    fit_intercept=True,\n",
    "    normalize=False,\n",
    "    precompute=False,\n",
    "    copy_X=True,\n",
    "    max_iter=1000,\n",
    "    tol=0.0001,\n",
    "    random_state=None)  \n",
    "    >  \n",
    "    > RidgeCV(alphas=(0.1, 1.0, 10.0),\n",
    "    *,\n",
    "    fit_intercept=True,\n",
    "    normalize=False,\n",
    "    scoring=None,\n",
    "    cv=None,\n",
    "    gcv_mode=None,\n",
    "    store_cv_values=False,)   \n",
    "    \n",
    "3. 多项式回归使用PolynomialFeatures做特征工程实现   \n",
    "    > from sklearn.preprocessing import PolynomialFeatures  \n",
    "    > poly = PolynomialFeatures(degree=2, interaction_only=False, include_bias=True, order='C')  \n",
    "    > X_train_poly = poly.fit_transform(X_train)  \n",
    "    > X_test_poly = poly.transform(X_test)  \n",
    "\n",
    "4. 正规化Normalizer和标准化StandardScaler\n",
    "    > from sklearn.preprocessing import StandardScaler, Normalizer  \n",
    "    >  \n",
    "    > scaler = StandardScaler(copy=True, with_mean=True, with_std=True)  \n",
    "    > X_train_scaler = scaler.fit_transform(X_train)  \n",
    "    > X_test_scaler = scaler.transform(X_test)  \n",
    "    >    \n",
    "    > norm = Normalizer(norm=\"l2\", copy=True)  \n",
    "    > X_train_norm = norm.fit_transform(X_train)  \n",
    "    > X_test_norm = norm.transform(X_test) \n",
    "    >  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 作业  \n",
    "\n",
    "1. 熟悉每个模型的各个参数  \n",
    "2. 三种归一化有什么区别？什么时候用Normalizer，什么时候用StandardScaler，什么时候用MinMaxScaler？ \n",
    "3. 试着用numpy实现PolynomialFeatures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 相关链接  \n",
    "  \n",
    "<a href=\"./02.1.LinearRegression.ipynb\" style=\"\"> 2.1 线性回归、岭回归、Lasso、SGD、局部加权线性回归原理</a>  \n",
    "  \n",
    "<a href=\"./02.3.LinearRegression-numpy.ipynb\" style=\"\"> 2.3 numpy实现线性回归、岭回归、SGD回归</a>  \n",
    "<a href=\"./02.4.LinearRegression-tf2.ipynb\"> 2.4 TensorFlow2实现线性回归、岭回归、SGD回归 </a>  \n",
    "<a href=\"./02.5.LinearRegression-torch1.ipynb\"> 2.5 PyTorch1实现线性回归、岭回归、SGD回归 </a>  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 项目源码  \n",
    "\n",
    "https://github.com/LossJ     \n",
    "进入后点击Statistic-Machine-Learning"
   ]
  }
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